MATH 540- WEEK 11 FINAL EXAM 100%

Question 6 5 out of 5 points In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 – x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected. Answer Selected Answer: False Correct Answer: False Question 7 5 out of 5 points Events that cannot occur at the same time in any trial of an experiment are: Answer Selected Answer: Correct Answer: mutually exclusive mutually exclusive Question 8 5 out of 5 points Using the minimax regret criterion to make a decision, you Answer Selected Answer: Construct a table of regrets. Look at the maximum regret for each decision. Select the decision with the smallest maximum regret. Correct Answer: Construct a table of regrets. Look at the maximum regret for each decision. Select the decision with the smallest maximum regret. Question 9 5 out of 5 points The probability of observing x successes in a fixed number of trials is a problem related to Answer Selected Answer: Correct Answer: the binomial distribution the binomial distribution Question 10 5 out of 5 points Using the maximin criterion to make a decision, you Answer Selected Answer: Look at the worst payoff for each possible decision and select the decision with the largest worst payoff Correct Answer: Look at the worst payoff for each possible decision and select the decision with the largest worst payoff Question 11 5 out of 5 points A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. The conservative (maximin) strategy is: Answer Selected Answer: Correct Answer: Lease Lease Question 12 5 out of 5 points Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the storage space constraint? Answer Selected Answer: Correct Answer: 100B + 80M ≤ 18000 100B + 80M ≤ 18000 Question 13 5 out of 5 points Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased? Answer Selected Answer: B = 0, M = 225 Correct Answer: B = 0, M = 225 Question 14 5 out of 5 points Given the following linear programming problem that minimizes cost. Min Z = 2x + 8y Subject to 8x + 4y ≥ 64 2x + 4y ≥ 32 y ≥ 2 What is the sensitivity range for the third constraint, y ≥ 2? Answer Selected Answer: Correct Answer: 0 to 5.33 0 to 5.33 Question 15 5 out of 5 points For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: Answer Selected Answer: Correct Answer: same product mix, different total profit same product mix, different total profit Question 16 5 out of 5 points In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct? Answer Selected Answer: Correct Answer: X1 ≤ 0.35(X1 + X2 + X3) X1 ≤ 0.35(X1 + X2 + X3) Question 17 5 out of 5 points The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient. Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds) 1 20 24 30 2 30 10 50 3 0 30 20 4 24 15 60 5 10 20 40 The constraint for ingredient 3 is: Answer Selected Answer: .3B ≥ 20 Correct Answer: .3B ≥ 20 Question 18 5 out of 5 points The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 different machines that can produce this kind of hose. Write the constraint that indicates they have to use at least three of the five machines in their production. Answer Selected Answer: Correct Answer: Y1 + Y2 + Y3 + Y4 + Y5 ≥ 3 Y1 + Y2 + Y3 + Y4 + Y5 ≥ 3 Question 19 5 out of 5 points If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a constraint. Answer Selected Answer: Correct Answer: corequisite corequisite Question 20 0 out of 5 points A professor needs help from 3 student helpers to complete 4 tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below. Which of the following constraints represents the assignment for student A? Answer Selected Answer: Correct Answer: XA1 +XA2 + XA3 + XA4 ≥ 0 XA1 +XA2 + XA3 + XA4 = 1 Question 21 0 out of 5 points Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to 2. Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. Supply is less than demand, so this is an unbalanced transshipment model. Which constraint represents the quantity shipped to retail outlet 6? Answer Selected Answer: Correct Answer: X23 + X36 = 450 X36 + X26 ≤ 450 Question 22 5 out of 5 points Professor Dewey would like to assign grades such that 15% of students receive As. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.) Answer Selected Answer: 75 Correct Answer: 75 Question 23 5 out of 5 points Jack is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. The decisions of each university have no effect on each other. This means that they are: Answer Selected Answer: Correct Answer: independent independent Question 24 5 out of 5 points Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing? Answer Selected Answer: Correct Answer: 62.5 62.5 Question 25 5 out of 5 points For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of: Answer Selected Answer: 2 Correct Answer: 2 Question 26 5 out of 5 points moving averages react more slowly to recent demand changes than do moving averages. Answer Selected Answer: Correct Answer: Longer-period, shorter-period Longer-period, shorter-period Question 27 5 out of 5 points Consider the following graph of sales. Which of the following characteristics is exhibited by the data? Answer Selected Answer: Correct Answer: Trend plus irregular Trend plus irregular Question 28 5 out of 5 points Joseph is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. What is the probability that Jim will not be accepted at either university? (Note: write your answer as a probability, with two decimal places. If necessary, round to two decimal places. For instance, a probability of 0.252 should be written as 0.25). Answer Selected Answer: 0.28 Correct Answer: Evaluation Method Correct Answer Case Sensitivity Exact Match 0.28 Question 29 5 out of 5 points Nixon’s Bed and Breakfast has a fixed cost of $5000 per month and the revenue they receive from each booked room is $200. The variable cost per room is $75. How many rooms do they have to sell each month to break even? (Note: The answer is a whole number. Give the answer as a whole number, omitting the decimal point. For instance, use 12 for twelve rooms). Answer Selected Answer: 40 Correct Answer: Evaluation Method Correct Answer Case Sensitivity Exact Match 40 Question 30 5 out of 5 points Ford’s Bed & Breakfast breaks even if they sell 50 rooms each month. They have a fixed cost of $6500 per month. The variable cost per room is $30. For this model to work, what must be the revenue per room? (Note: The answer is a whole dollar amount. Give the answer as a whole number, omitting the decimal point. For instance, use 105 to write $105.00). Answer Selected Answer: 160 Correct Answer: Evaluation Method Correct Answer Case Sensitivity Exact Match 160 Question 31 0 out of 5 points Consider the following linear program, which maximizes profit for two products, regular (R), and super (S): MAX 50R + 75S s.t. 1.2R + 1.6 S ≤ 600 assembly (hours) 0.8R + 0.5 S ≤ 300 paint (hours) .16R + 0.4 S ≤ 100 inspection (ho