Introduction to Management Science A Modeling 6e TB

1 Copyright © 2019 McGraw-Hill Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 1 Introduction 1) Managers need to know the mathematical theory behind the techniques of management science so that they can lead management science teams. 2) Management scientists use mathematical techniques to make decisions, which are then implemented by managers. 3) Spreadsheets allow many managers to conduct their own analyses in management science studies. 4) Managers must rely on management science experts to create and understand managerial problems. 5) Management science is a discipline that attempts to aid managerial decision making by applying a scientific approach to managerial problems that involve quantitative factors. 6) The discovery of the simplex method in 1947 was the beginning of management science as a discipline. 7) The rapid growth of computing capability and power has led to a corresponding rapid growth of the management science discipline. 8) Managers make decisions based solely on the quantitative factors involved in the problem. 9) A management science team will try to conduct a systematic investigation of a problem that includes careful data gathering, developing and testing hypotheses, and then applying sound logic in the analysis. 10) The mathematical model of a business problem is the system of equations and related mathematical expressions that describes the essence of the problem. 11) A mathematical model of a business problem allows a manager to evaluate both quantitative and qualitative aspects of the problem. 12) Once management makes its decisions, the management science team typically is finished with its involvement in the problem. 13) A cost that varies with the production volume would be a fixed cost. 14) A cost that varies with the production volume would be a variable cost. 15) A cost that does not vary with the production volume would be a fixed cost. 16) A cost that does not vary with the production volume would be a variable cost. 2 Copyright © 2019 McGraw-Hill 17) At the break-even point, management is indifferent between producing a product and not producing it. 18) The best way to solve a break-even problem with a spreadsheet model is to try different production quantities until the quantity that leads to profits of zero is found. 19) A constraint is an algebraic variable that represents a quantifiable decision to be made. 20) A decision variable is an algebraic variable that represents a quantifiable decision to be made. 21) A parameter in a model is a variable that represents a decision to be made. 22) The objective function for a model is a mathematical expression of the measure of performance for the problem in terms of the decision variables. 23) Sensitivity analysis is used to check the effect of changes in the model. 24) Investigating the potential outcomes when estimates turn out to be incorrect is known as "what-if analysis." 25) "What-if analysis" is a process used to generate estimates for use in mathematical models. 26) Enlightened future managers should know which of the following? A) The power and relevance of management science. B) When management science can and cannot be applied. C) How to apply the major techniques of management science. D) How to interpret the results of a management science study. E) All of the answer choices are correct. 27) The rapid development of the management science discipline can be credited in part to: A) World War I. B) George Dantzig. C) the computer revolution. D) George Dantzig and the computer revolution. E) World War I, George Dantzig, and the computer revolution. 28) Managers may base their decisions on which of the following? A) Quantitative factors. B) Their best judgment. C) Opinions from other managers. D) Past experience. E) All of the answer choices are correct. 3 Copyright © 2019 McGraw-Hill 29) Management science is based strongly on which of the following fields? A) Mathematics. B) Computer science. C) Business administration. D) Mathematics and computer science only. E) All of the answer choices are correct. 30) Which of the following are components of a mathematical model for decision making? A) Decision variables. B) An objective function. C) Constraints. D) Parameters. E) All of the answer choices are correct. 31) Which of the following are steps in a typical management science study? A) Define the problem and gather data. B) Formulate a model to represent the problem. C) Test the model and refine it as needed. D) Help to implement the recommendations. E) All of the answer choices are correct. 32) Which of the following is a mathematical expression that gives the measure of performance for the problem? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. 33) Which of the following is a constant in a mathematical model? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. 34) Which of the following is an inequality or equation that expresses a restriction in a mathematical model? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. 4 Copyright © 2019 McGraw-Hill 35) A manager has determined that a potential new product can be sold at a price of $10.00 each. The cost to produce the product is $5.00, but the equipment necessary for production must be leased for $25,000 per year. What is the break-even point? A) 2,500 units. B) 5,000 units. C) 7,500 units. D) 10,000 units. E) 25,000 units. 36) In order to produce a new product, a firm must lease equipment at a cost of $10,000 per year. The managers feel that they can sell 5,000 units per year at a price of $7.50. What is the highest variable cost that will allow the firm to at least break even on this project? A) $2.50. B) $3.50. C) $4.50. D) $5.50. E) $6.50. 37) A manager has determined that a potential new product can be sold at a price of $20.00 each. The cost to produce the product is $10.00, but the equipment necessary for production must be leased for $75,000 per year. What is the break-even point? A) 2,500 units. B) 5,000 units. C) 7,500 units. D) 10,000 units. E) 25,000 units. 38) Production has indicated that they can produce widgets at a cost of $4.00 each if they lease new equipment at a cost of $10,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project? A) 4,000 units at $5.00 each. B) 3,000 units at $7.50 each. C) 1,500 units at $10.00 each. D) 1,000 units at $15.00 each E) 25,000 units. 39) A manager has determined that a potential new product can be sold at a price of $50.00 each. The cost to produce the product is $35.00, but the equipment necessary for production must be leased for $100,000 per year. What is the break-even point? A) 3,333 units. B) 5,000 units. C) 6,667 units. D) 7,500 units. E) 8,167 units. 5 Copyright © 2019 McGraw-Hill 40) In order to produce a new product, a firm must lease equipment at a cost of $25,000 per year. The managers feel that they can sell 10,000 units per year at a price of $15.00. What is the highest variable cost that will allow the firm to at least break even on this project? A) $12.50. B) $13.50. C) $14.50. D) $15.50. E) $16.50. 41) A manager has determined that a potential new product can be sold at a price of $100.00 each. The cost to produce the product is $75.00, but the equipment necessary for production must be leased for $175,000 per year. What is the break-even point? A) 3,000 units. B) 5,000 units. C) 7,000 units. D) 10,000 units. E) 25,000 units. 42) Production has indicated that they can produce widgets at a cost of $3.00 each if they lease new equipment at a cost of $10,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project? A) 7,500 units at $17.50 each. B) 4,000 units at $20.00 each. C) 3,000 units at $22.50 each. D) 2,500 units at $25.00 each E) 1,500 units at $27.50 each. 43) When evaluating a project to determine the break-even quantity, the advantage of a spreadsheet model is? A) Users can't see the formulas used. B) Calculations are always rounded to the nearest integer. C) The analyst can use Excel's "BREAKEVEN" function to perform the calculation D) A number of different estimates can be quickly evaluated once the model is constructed. E) There are no advantages to spreadsheet modeling of break-even analysis. 44) Which of the following is TRUE about the break-even point? A) When sales are equal to the break-even point, profit will be zero. B) When sales exceed the break-even point, profits will be negative. C) When sales are below the break-even point, profits will be positive. D) Once sales exceed the break-even point, profits no longer change if sales increase further. E) The total revenue and total cost are equal at the point where profits are maximized. 6 Copyright © 2019 McGraw-Hill 45) Which of the following statements about the break-even quantity is FALSE? A) When sales are equal to the break-even point, profit will be zero. B) When sales exceed the break-even point, profits will be positive. C) When sales are below the break-even point, profits will be negative. D) Once sales exceed the break-even point, profits continue to increase as sales increase. E) The total revenue and total cost are equal at the point where profits are maximized. 46) Business analytics is a field which. A) is the same as operations research. B) aids managerial decision making through the use of data. C) uses descriptive analytics to predict the future. D) uses prescriptive analytics to analyze trends. E) uses predictive analytics to determine the best course of action. 47) Descriptive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. 48) Predictive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. 49) Prescriptive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. 50) In order to produce a new product, a firm must lease new equipment. The managers feel that they can sell 10,000 units per year at a price of $7.50. If the variable cost of production is $5.00 per unit, what is the most the firm can spend to lease the new equipment without losing money? A) $10,000. B) $15,000. C) $20,000. D) $25,000. E) $30,000. 7 Copyright © 2019 McGraw-Hill 51) A group is planning a conference. The cost to rent the space is $1,000. Each attendee will be charged $50.00 to attend, but the group provides a lunch (the group will pay $10.00 for each lunch). What is the break-even point? A) 20 attendees. B) 25 attendees. C) 30 attendees. D) 35 attendees. E) 40 attendees. 52) A training firm is planning to offer a one-day class at a local facility. The class is projected to have 50 students, each of whom will pay $25.00 to attend. The firm provides materials to each student (materials cost the firm $10.00 per student). What is the most the firm can afford to pay to rent the facility for one day? A) $250. B) $500. C) $750. D) $1,000. E) $1,250. 53) A tour company is planning a bus trip to a local museum. The company will lease a bus from a local bus owner for $400 and estimates that it will spend $15.00 per person for admission and lunch. Which of the following volume/price alternatives will allow the firm to avoid losing money on the trip? A) 20 customers at $30.00 each. B) 30 customers at $27.50 each. C) 40 customers at $25.00 each. D) 50 customers at $22.50 each E) 60 customers at $20.00 each. 54) You have decided to start a vending machine business. A local store has space available for your machine but wants to charge you an annual fee to use the space. You estimate that you can sell 5,000 cans of soda each year. You sell a can of soda for $1.25, which allows you a profit of $0.50 per can. What is the most you would spend to lease the space for one year? A) $1,000. B) $2,500. C) $5,000. D) $7,500. E) $10,000. 1 Copyright © 2019 McGraw-Hill Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 1 Introduction 1) Managers need to know the mathematical theory behind the techniques of management science so that they can lead management science teams. Answer: FALSE Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application 2) Management scientists use mathematical techniques to make decisions, which are then implemented by managers. Answer: FALSE Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application 3) Spreadsheets allow many managers to conduct their own analyses in management science studies. Answer: TRUE Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application 4) Managers must rely on management science experts to create and understand managerial problems. Answer: FALSE Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application 2 Copyright © 2019 McGraw-Hill 5) Management science is a discipline that attempts to aid managerial decision making by applying a scientific approach to managerial problems that involve quantitative factors. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 6) The discovery of the simplex method in 1947 was the beginning of management science as a discipline. Answer: FALSE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 7) The rapid growth of computing capability and power has led to a corresponding rapid growth of the management science discipline. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 8) Managers make decisions based solely on the quantitative factors involved in the problem. Answer: FALSE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 3 Copyright © 2019 McGraw-Hill 9) A management science team will try to conduct a systematic investigation of a problem that includes careful data gathering, developing and testing hypotheses, and then applying sound logic in the analysis. Answer: TRUE Difficulty: 3 Hard Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Apply AACSB: Reflective Thinking 10) The mathematical model of a business problem is the system of equations and related mathematical expressions that describes the essence of the problem. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 11) A mathematical model of a business problem allows a manager to evaluate both quantitative and qualitative aspects of the problem. Answer: FALSE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 12) Once management makes its decisions, the management science team typically is finished with its involvement in the problem. Answer: FALSE Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application 4 Copyright © 2019 McGraw-Hill 13) A cost that varies with the production volume would be a fixed cost. Answer: FALSE Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Understand AACSB: Knowledge Application 14) A cost that varies with the production volume would be a variable cost. Answer: TRUE Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Understand AACSB: Knowledge Application 15) A cost that does not vary with the production volume would be a fixed cost. Answer: TRUE Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Understand AACSB: Knowledge Application 16) A cost that does not vary with the production volume would be a variable cost. Answer: FALSE Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Understand AACSB: Knowledge Application 17) At the break-even point, management is indifferent between producing a product and not producing it. Answer: TRUE Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 5 Copyright © 2019 McGraw-Hill 18) The best way to solve a break-even problem with a spreadsheet model is to try different production quantities until the quantity that leads to profits of zero is found. Answer: FALSE Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a spreadsheet model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 19) A constraint is an algebraic variable that represents a quantifiable decision to be made. Answer: FALSE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 20) A decision variable is an algebraic variable that represents a quantifiable decision to be made. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 21) A parameter in a model is a variable that represents a decision to be made. Answer: FALSE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 22) The objective function for a model is a mathematical expression of the measure of performance for the problem in terms of the decision variables. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 6 Copyright © 2019 McGraw-Hill 23) Sensitivity analysis is used to check the effect of changes in the model. Answer: TRUE Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 24) Investigating the potential outcomes when estimates turn out to be incorrect is known as "what-if analysis." Answer: TRUE Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 25) "What-if analysis" is a process used to generate estimates for use in mathematical models. Answer: FALSE Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 26) Enlightened future managers should know which of the following? A) The power and relevance of management science. B) When management science can and cannot be applied. C) How to apply the major techniques of management science. D) How to interpret the results of a management science study. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 7 Copyright © 2019 McGraw-Hill 27) The rapid development of the management science discipline can be credited in part to: A) World War I. B) George Dantzig. C) the computer revolution. D) George Dantzig and the computer revolution. E) World War I, George Dantzig, and the computer revolution. Answer: D Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Define the term management science Bloom's: Remember AACSB: Knowledge Application 28) Managers may base their decisions on which of the following? A) Quantitative factors. B) Their best judgment. C) Opinions from other managers. D) Past experience. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 29) Management science is based strongly on which of the following fields? A) Mathematics. B) Computer science. C) Business administration. D) Mathematics and computer science only. E) All of the answer choices are correct. Answer: D Difficulty: 1 Easy Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Remember AACSB: Knowledge Application 8 Copyright © 2019 McGraw-Hill 30) Which of the following are components of a mathematical model for decision making? A) Decision variables. B) An objective function. C) Constraints. D) Parameters. E) All of the answer choices are correct. Answer: E Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 31) Which of the following are steps in a typical management science study? A) Define the problem and gather data. B) Formulate a model to represent the problem. C) Test the model and refine it as needed. D) Help to implement the recommendations. E) All of the answer choices are correct. Answer: E Difficulty: 2 Medium Topic: The Nature of Management Science Learning Objective: Describe the nature of management science Bloom's: Understand AACSB: Knowledge Application 32) Which of the following is a mathematical expression that gives the measure of performance for the problem? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. Answer: C Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 9 Copyright © 2019 McGraw-Hill 33) Which of the following is a constant in a mathematical model? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. Answer: B Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 34) Which of the following is an inequality or equation that expresses a restriction in a mathematical model? A) Decision variable. B) Parameter. C) Objective function. D) Constraint. E) None of the answer choices are correct. Answer: D Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Explain what a mathematical model is Bloom's: Remember AACSB: Knowledge Application 35) A manager has determined that a potential new product can be sold at a price of $10.00 each. The cost to produce the product is $5.00, but the equipment necessary for production must be leased for $25,000 per year. What is the break-even point? A) 2,500 units. B) 5,000 units. C) 7,500 units. D) 10,000 units. E) 25,000 units. Answer: B Explanation: Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Apply AACSB: Knowledge Application 10 Copyright © 2019 McGraw-Hill 36) In order to produce a new product, a firm must lease equipment at a cost of $10,000 per year. The managers feel that they can sell 5,000 units per year at a price of $7.50. What is the highest variable cost that will allow the firm to at least break even on this project? A) $2.50. B) $3.50. C) $4.50. D) $5.50. E) $6.50. Answer: D Explanation: , therefore Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Analyze AACSB: Analytical Thinking 37) A manager has determined that a potential new product can be sold at a price of $20.00 each. The cost to produce the product is $10.00, but the equipment necessary for production must be leased for $75,000 per year. What is the break-even point? A) 2,500 units. B) 5,000 units. C) 7,500 units. D) 10,000 units. E) 25,000 units. Answer: C Explanation: Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 11 Copyright © 2019 McGraw-Hill 38) Production has indicated that they can produce widgets at a cost of $4.00 each if they lease new equipment at a cost of $10,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project? A) 4,000 units at $5.00 each. B) 3,000 units at $7.50 each. C) 1,500 units at $10.00 each. D) 1,000 units at $15.00 each E) 25,000 units. Answer: B Explanation: Calculating the break-even for each price, it is clear that 3,000 units at $7.50 each is the only option where the sales forecast exceeds the break-even point. Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Evaluate AACSB: Analytical Thinking 12 Copyright © 2019 McGraw-Hill 39) A manager has determined that a potential new product can be sold at a price of $50.00 each. The cost to produce the product is $35.00, but the equipment necessary for production must be leased for $100,000 per year. What is the break-even point? A) 3,333 units. B) 5,000 units. C) 6,667 units. D) 7,500 units. E) 8,167 units. Answer: C Explanation: Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Apply AACSB: Knowledge Application 40) In order to produce a new product, a firm must lease equipment at a cost of $25,000 per year. The managers feel that they can sell 10,000 units per year at a price of $15.00. What is the highest variable cost that will allow the firm to at least break even on this project? A) $12.50. B) $13.50. C) $14.50. D) $15.50. E) $16.50. Answer: A Explanation: therefore Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Analyze AACSB: Analytical Thinking 13 Copyright © 2019 McGraw-Hill 41) A manager has determined that a potential new product can be sold at a price of $100.00 each. The cost to produce the product is $75.00, but the equipment necessary for production must be leased for $175,000 per year. What is the break-even point? A) 3,000 units. B) 5,000 units. C) 7,000 units. D) 10,000 units. E) 25,000 units. Answer: C Explanation: Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Analytical Thinking 14 Copyright © 2019 McGraw-Hill 42) Production has indicated that they can produce widgets at a cost of $3.00 each if they lease new equipment at a cost of $10,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project? A) 7,500 units at $17.50 each. B) 4,000 units at $20.00 each. C) 3,000 units at $22.50 each. D) 2,500 units at $25.00 each E) 1,500 units at $27.50 each. Answer: D Explanation: Calculating the break-even for each price, it is clear that 2,500 units at $25.00 each is the only option where the sales forecast equals the break-even point. Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Evaluate AACSB: Analytical Thinking 15 Copyright © 2019 McGraw-Hill 43) When evaluating a project to determine the break-even quantity, the advantage of a spreadsheet model is? A) Users can't see the formulas used. B) Calculations are always rounded to the nearest integer. C) The analyst can use Excel's "BREAKEVEN" function to perform the calculation D) A number of different estimates can be quickly evaluated once the model is constructed. E) There are no advantages to spreadsheet modeling of break-even analysis. Answer: D Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a spreadsheet model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 44) Which of the following is TRUE about the break-even point? A) When sales are equal to the break-even point, profit will be zero. B) When sales exceed the break-even point, profits will be negative. C) When sales are below the break-even point, profits will be positive. D) Once sales exceed the break-even point, profits no longer change if sales increase further. E) The total revenue and total cost are equal at the point where profits are maximized. Answer: A Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Remember AACSB: Knowledge Application 45) Which of the following statements about the break-even quantity is FALSE? A) When sales are equal to the break-even point, profit will be zero. B) When sales exceed the break-even point, profits will be positive. C) When sales are below the break-even point, profits will be negative. D) Once sales exceed the break-even point, profits continue to increase as sales increase. E) The total revenue and total cost are equal at the point where profits are maximized. Answer: A Difficulty: 1 Easy Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Understand AACSB: Knowledge Application 16 Copyright © 2019 McGraw-Hill 46) Business analytics is a field which. A) is the same as operations research. B) aids managerial decision making through the use of data. C) uses descriptive analytics to predict the future. D) uses prescriptive analytics to analyze trends. E) uses predictive analytics to determine the best course of action. Answer: B Difficulty: 1 Easy Topic: The Relationship between Analytics and Management Science Learning Objective: Describe the relationship between analytics and management science Bloom's: Remember AACSB: Knowledge Application 47) Descriptive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. Answer: A Difficulty: 1 Easy Topic: The Relationship between Analytics and Management Science Learning Objective: Describe the relationship between analytics and management science Bloom's: Remember AACSB: Knowledge Application 48) Predictive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. Answer: B Difficulty: 1 Easy Topic: The Relationship between Analytics and Management Science Learning Objective: Describe the relationship between analytics and management science Bloom's: Remember AACSB: Knowledge Application 17 Copyright © 2019 McGraw-Hill 49) Prescriptive analytics is the process of using data to. A) analyze trends. B) predict what will happen in the future. C) determine the break-even point. D) solve linear programming problems. E) determine the best course of action for the future. Answer: E Difficulty: 1 Easy Topic: The Relationship between Analytics and Management Science Learning Objective: Describe the relationship between analytics and management science Bloom's: Remember AACSB: Knowledge Application 50) In order to produce a new product, a firm must lease new equipment. The managers feel that they can sell 10,000 units per year at a price of $7.50. If the variable cost of production is $5.00 per unit, what is the most the firm can spend to lease the new equipment without losing money? A) $10,000. B) $15,000. C) $20,000. D) $25,000. E) $30,000. Answer: D Explanation: therefore If the firm has lease costs of $25,000 or less the product will not lose money. Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Analyze AACSB: Analytical Thinking 18 Copyright © 2019 McGraw-Hill 51) A group is planning a conference. The cost to rent the space is $1,000. Each attendee will be charged $50.00 to attend, but the group provides a lunch (the group will pay $10.00 for each lunch). What is the break-even point? A) 20 attendees. B) 25 attendees. C) 30 attendees. D) 35 attendees. E) 40 attendees. Answer: B Explanation: Difficulty: 2 Medium Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Apply AACSB: Knowledge Application 52) A training firm is planning to offer a one-day class at a local facility. The class is projected to have 50 students, each of whom will pay $25.00 to attend. The firm provides materials to each student (materials cost the firm $10.00 per student). What is the most the firm can afford to pay to rent the facility for one day? A) $250. B) $500. C) $750. D) $1,000. E) $1,250. Answer: C Explanation: , therefore If the firm has rental costs of $750 or less the product will not lose money. Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Analyze AACSB: Analytical Thinking 19 Copyright © 2019 McGraw-Hill 53) A tour company is planning a bus trip to a local museum. The company will lease a bus from a local bus owner for $400 and estimates that it will spend $15.00 per person for admission and lunch. Which of the following volume/price alternatives will allow the firm to avoid losing money on the trip? A) 20 customers at $30.00 each. B) 30 customers at $27.50 each. C) 40 customers at $25.00 each. D) 50 customers at $22.50 each E) 60 customers at $20.00 each. Answer: C Explanation: Calculating the break-even for each price, it is clear that 40 customers at $25.00 each is the only option where the sales forecast meets or exceeds the break-even point. Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Evaluate AACSB: Analytical Thinking 20 Copyright © 2019 McGraw-Hill 54) You have decided to start a vending machine business. A local store has space available for your machine but wants to charge you an annual fee to use the space. You estimate that you can sell 5,000 cans of soda each year. You sell a can of soda for $1.25, which allows you a profit of $0.50 per can. What is the most you would spend to lease the space for one year? A) $1,000. B) $2,500. C) $5,000. D) $7,500. E) $10,000. Answer: B Explanation: Since your price is $1.25 and your profit is $0.50, your cost per unit must be $1.25 – $0.50 = $0.75. , therefore If the store will lease the space for $2,500 or less the project will not lose money. Difficulty: 3 Hard Topic: An Illustration of the Management Science Approach: Break-Even Analysis Learning Objective: Use a mathematical model to perform a break-even analysis Bloom's: Analyze AACSB: Analytical Thinking 1 Copyright © 2019 McGraw-Hill Intro to Management Science: Modeling and Case Studies, 6e (Hillier) Chapter 2 Linear Programming: Basic Concepts 1) Linear programming problems may have multiple goals or objectives specified. 2) Linear programming allows a manager to find the best mix of activities to pursue and at what levels. 3) Linear programming problems always involve either maximizing or minimizing an objective function. 4) All linear programming models have an objective function and at least two constraints. 5) Constraints limit the alternatives available to a decision maker. 6) When formulating a linear programming problem on a spreadsheet, the data cells will show the optimal solution. 7) When formulating a linear programming problem on a spreadsheet, objective cells will show the levels of activities for the decisions being made. 8) When formulating a linear programming problem on a spreadsheet, the Excel equation for each output cell can typically be expressed as a SUMPRODUCT function. 9) One of the great strengths of spreadsheets is their flexibility for dealing with a wide variety of problems. 10) Linear programming problems can be formulated both algebraically and on spreadsheets. 11) The parameters of a model are the numbers in the data cells of a spreadsheet. 12) An example of a decision variable in a linear programming problem is profit maximization. 13) A feasible solution is one that satisfies all the constraints of a linear programming problem simultaneously. 14) An infeasible solution violates all of the constraints of the problem. 15) The best feasible solution is called the optimal solution. 16) Since all linear programming models must contain nonnegativity constraints, Solver will automatically include them and it is not necessary to add them to a formulation. 17) The line forming the boundary of what is permitted by a constraint is referred to as a parameter. 18) The origin satisfies any constraint with a ≥ sign and a positive right-hand side. 2 Copyright © 2019 McGraw-Hill 19) The feasible region only contains points that satisfy all constraints. 20) A circle would be an example of a feasible region for a linear programming problem. 21) The equation 5x + 7y = 10 is linear. 22) The equation 3xy = 9 is linear. 23) The graphical method can handle problems that involve any number of decision variables. 24) An objective function represents a family of parallel lines. 25) When solving linear programming problems graphically, there are an infinite number of possible objective function lines. 26) For a graph where the horizontal axis represents the variable x and the vertical axis represents the variable y, the slope of a line is the change in y when x is increased by 1. 27) The value of the objective function decreases as the objective function line is moved away from the origin. 28) A feasible point on the optimal objective function line is an optimal solution. 29) A linear programming problem can have multiple optimal solutions. 30) All constraints in a linear programming problem are either ≤ or ≥ inequalities. 31) Linear programming models can have either ≤ or ≥ inequality constraints but not both in the same problem. 32) A maximization problem can generally be characterized by having all ≥ constraints. 33) If a single optimal solution exists while using the graphical method to solve a linear programming problem, it will exist at a corner point. 34) When solving a maximization problem graphically, it is generally the goal to move the objective function line out, away from the origin, as far as possible. 35) When solving a minimization problem graphically, it is generally the goal to move the objective function line out, away from the origin, as far as possible. 36) A manager should know the following things about linear programming. A) What it is. B) When it should be used. C) When it should not be used. D) How to interpret the results of a study. E) All of the answer choices are correct. 3 Copyright © 2019 McGraw-Hill 37) Which of the following is not a component of a linear programming model? A) constraints B) decision variables C) parameters D) an objective E) a spreadsheet 38) In linear programming, solutions that satisfy all of the constraints simultaneously are referred to as: A) optimal. B) feasible. C) nonnegative. D) targeted. E) All of the answer choices are correct. 39) When formulating a linear programming problem on a spreadsheet, which of the following is true? A) Parameters are called data cells. B) Decision variables are called changing cells. C) Nonnegativity constraints must be included. D) The objective function is called the objective cell. E) All of the answer choices are correct. 40) Where are the data cells located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct. 4 Copyright © 2019 McGraw-Hill 41) Where are the changing cells located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct. 42) Where is the objective cell located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct. 5 Copyright © 2019 McGraw-Hill 43) Where are the output cells located? A) B2:C2 B) B2:C2, B5:C7, and F5:F7 C) B10:C10 D) F10 E) None of the answer choices are correct. 44) Which of the following could not be a constraint for a linear programming problem? A) 1A + 2B ≤ 3 B) 1A + 2B ≥ 3 C) 1A + 2B = 3 D) 1A + 2B E) 1A + 2B + 3C ≤ 3 45) For the products A, B, C, and D, which of the following could be a linear programming objective function? A) P = 1A + 2B +3C + 4D B) P = 1A + 2BC +3D C) P = 1A + 2AB +3ABC + 4ABCD D) P = 1A + 2B/C +3D E) All of the answer choices are correct. 46) After the data is collected the next step to formulating a linear programming model is to: A) identify the decision variables. B) identify the objective function. C) identify the constraints. D) specify the parameters of the problem. E) None of the answer choices are correct. 47) When using the graphical method, the region that satisfies all of the constraints of a linear programming problem is called the: A) optimum solution space. B) region of optimality. C) profit maximization space. D) feasible region. E) region of nonnegativity. 6 Copyright © 2019 McGraw-Hill 48) Solving linear programming problems graphically A) is possible with any number of decision variables. B) provides geometric intuition about what linear programming is trying to achieve. C) will always result in an optimal solution. D) All of the answers choices are correct. E) None of the answers choices are correct. 49) Which objective function has the same slope as this one: 4x + 2y = 20. A) 2x + 4y = 20 B) 2x − 4y = 20 C) 4x − 2y = 20 D) 8x + 8y = 20 E) 4x + 2y = 10 50) Given the following 2 constraints, which solution is a feasible solution for a maximization problem? (1) 14x1 + 6x2 ≤ 42 (2) x1 − x2 ≤ 3 A) (x1, x2) = (1, 5) B) (x1, x2) = (5, 1) C) (x1, x2) = (4, 4) D) (x1, x2) = (2, 1) E) (x1, x2) = (2, 6) 51) Which of the following constitutes a simultaneous solution to the following 2 equations? (1) 3x1 + 4x2 = 10 (2) 5x1 + 4x2 = 14 A) (x1, x2) = (2, 0.5) B) (x1, x2) = (4, 0.5) C) (x1, x2) = (2, 1) D) x1 = x2 E) x2 = 2x1 7 Copyright © 2019 McGraw-Hill 52) Which of the following constitutes a simultaneous solution to the following 2 equations? (1) 3x1 + 2x2 = 6 (2) 6x1 + 3x2 = 12 A) (x1, x2) = (1, 1.5) B) (x1, x2) = (0.5, 2) C) (x1, x2) = (0, 3) D) (x1, x2) = (2, 0) E) (x1, x2) = (0, 0) 53) What is the optimal solution for the following problem? Maximize P = 3x + 15y subject to 2x + 4y ≤ 12 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0. A) (x, y) = (2, 0) B) (x, y) = (0, 3) C) (x, y) = (0, 0) D) (x, y) = (1, 5) E) None of the answer choices are correct. 54) Given the following 2 constraints, which solution is a feasible solution for a minimization problem? (1) 14x1 + 6x2 ≥ 42 (2) x1 + 3x2 ≥ 6 A) (x1, x2) = (0.5, 5). B) (x1, x2) = (0, 4). C) (x1, x2) = (2, 5). D) (x1, x2) = (1, 2). E) (x1, x2) = (2, 1). 55) Use the graphical method for linear programming to find the optimal solution for the following problem. Minimize C = 3x + 15y subject to 2x + 4y ≥ 12 5x + 2y ≥ 10 and x ≥ 0, y ≥ 0. A) (x, y) = (0, 0). B) (x, y) = (0, 3). C) (x, y) = (0, 5). D) (x, y) = (1, 2.5). E) (x, y) = (6, 0). 8 Copyright © 2019 McGraw-Hill 56) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the objective function? A) P = A + 2B. B) P = 12A + 8B. C) P = 2A + B. D) P = 8A + 12B. E) P = 4A + 8B. 57) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the constraint for Colombian beans? A) A + 2B ≤ 4,800. B) 12A + 8B ≤ 4,800. C) 2A + B ≤ 4,800. D) 8A + 12B ≤ 4,800. E) 4A + 8B ≤ 4,800. 58) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the constraint for Dominican beans? A) 12A + 8B ≤ 4,800. B) 8A + 12B ≤ 4,800. C) 4A + 8B ≤ 3,200. D) 8A + 4B ≤ 3,200. E) 4A + 8B ≤ 4,800. 9 Copyright © 2019 McGraw-Hill 59) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. Which of the following is not a feasible solution? A) (A, B) = (0, 0). B) (A, B) = (0, 400). C) (A, B) = (200, 300). D) (A, B) = (400, 0). E) (A, B) = (400, 400). 60) The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the weekly profit when producing the optimal amounts? A) $0. B) $400. C) $700. D) $800. E) $900. 61) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. What is the objective function? A) P = 2L + 3D. B) P = 2L + 4D. C) P = 3L + 2D. D) P = 4L + 2D. E) P = 5L + 3D. 10 Copyright © 2019 McGraw-Hill 62) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. What is the time constraint? A) 2L +3D ≤ 480. B) 2L + 4D ≤ 480. C) 3L + 2D ≤ 480. D) 4L + 2D ≤ 480. E) 5L + 3D ≤ 480. 63) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. Which of the following is not a feasible solution? A) (L, D) = (0, 0). B) (L, D) = (0, 120). C) (L, D) = (90, 75). D) (L, D) = (135, 0). E) (L, D) = (135, 120). 64) The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg. The brewery's goal is to maximize profits. What is the daily profit when producing the optimal amounts? A) $0. B) $240. C) $420. D) $405. E) $505. 11 Copyright © 2019 McGraw-Hill 65) The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1,500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. The firm's goal is to maximize profits. What is the objective function? A) P = 4R + 6S B) P = 2R + 3S C) P = 6R + 4S D) P = 3R +2S E) P = 5R + 5S 66) What is the time constraint? A) 2R + 3S ≤ 720. B) 2R + 5S ≤ 720. C) 3R + 2S ≤ 720. D) 3R + 5S ≤ 720. E) 5R + 5S ≤ 720. 67) The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1,500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. The firm's goal is to maximize profits. Which of the following is not a feasible solution? A) (R, S) = (0, 0) B) (R, S) = (0, 240) C) (R, S) = (180, 120) D) (R, S) = (300, 0) E) (R, S) = (180, 240) 68) The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1,500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. The firm's goal is to maximize profits. What is the daily profit when producing the optimal amounts? A) $960 B) $1,560 C) $1,800 D) $1,900 E) $2,520 12 Copyright © 2019 McGraw-Hill 69) An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. What is the objective function? A) P = 4A + 1B B) P = 0.25A + 1B C) P = 1A + 4B D) P = 1A + 1B E) P = 0.25A + 0.5B 70) An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. What is the time constraint? A) 1A + 1B ≤ 800 B) 0.25A + 0.5B ≤ 800 C) 0.5A + 0.25B ≤ 800 D) 1A + 0.5B ≤ 800 E) 0.25A + 1B ≤ 800 71) An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. Which of the following is not a feasible solution? A) (A, B) = (0, 0) B) (A, B) = (0, 1000) C) (A, B) = (1800, 700) D) (A, B) = (2500, 0) E) (A, B) = (100, 1600) 13 Copyright © 2019 McGraw-Hill 72) An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each. The firm's goal is to maximize profits. What is the weekly profit when producing the optimal amounts? A) $10,000 B) $4,600 C) $2,500 D) $5,200 E) $6,400 73) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. What is the objective function? A) P = 0.3B + 0.2C. B) P = 0.6B + 0.3C. C) P = 0.2B + 0.3C. D) P = 0.2B + 0.4C. E) P = 0.1B + 0.1C. 74) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. What is the sugar constraint? A) 6B + 3C ≤ 4,800 B) 1B + 1C ≤ 4,800 C) 2B + 4C ≤ 4,800 D) 4B + 2C ≤ 4,800 E) 2B + 3C ≤ 4,800 14 Copyright © 2019 McGraw-Hill 75) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. Which of the following is not a feasible solution? A) (B, C) = (0, 0) B) (B, C) = (0, 1100) C) (B, C) = (800, 600) D) (B, C) = (1100, 0) E) (B, C) = (0, 1400) 76) A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. What is the daily profit when producing the optimal amounts? A) $580 B) $340 C) $220 D) $380 E) $420 77) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. What is the objective function? A) P = 0.5D + 0.4C B) P = 0.2D + 0.3C C) P = 0.4D + 0.5C D) P = 0.1D + 0.2C E) P = 0.6D + 0.8C 15 Copyright © 2019 McGraw-Hill 78) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. What is the sugar constraint? A) 2D + 3C ≤ 4,800 B) 6D + 8C ≤ 4,800 C) 1D + 2C ≤ 4,800 D) 3D + 2C ≤ 4,800 E) 4D + 5C ≤ 4,800 79) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. Which of the following is not a feasible solution? A) (D, C) = (0, 0) B) (D, C) = (0, 1000) C) (D, C) = (800, 600) D) (D, C) = (1600, 0) E) (D, C) = (0, 1,200) 80) The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker's, Inc. would like to maximize profits. What is the daily profit when producing the optimal amounts? A) $800 B) $500 C) $640 D) $620 E) $600 16 Copyright © 2019 McGraw-Hill 81) The operations manager of a mail order house purchases double (D) and twin (T) beds for resale. Each double bed costs $500 and requires 100 cubic feet of storage space. Each twin bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each double bed is $300 and