BUS 660 Topic 4 Midterm Exam (Summer Term)

1. Question:Which of the methods for decision making best protects the decision maker from undesirable results? 2. Question:If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (xi) or 125 wiffle balls (x?) can be produced per hour of labor, which of the following constraints reflects this situation? 3. Question:Problem 4-05 (Algorithmic) In American football, touchdowns are worth 6 points. After scoring a touchdown, the scoring team may subsequently attempt to score 1 or 2 additional points. Going for 1 point is virtually an assured success, while going for 2 points is successful only with probability p. Consider the following game situation. The Temple Wildcats are losing by 14 points to the Killeen Tigers near the end of regulation time. The only way for Temple to win (or tie) this game is to score two touchdowns while not allowing Killeen to score again. The Temple coach must decide whether to attempt a 1-point or 2-point conversion after each touchdown. If the score is tied at the end of regulation time, the game goes into overtime. The Temple coach believes that there is a 43% chance that Temple will win if the game goes into overtime. The probability of successfully converting a 1-point conversion is 1.0. The probability of successfully converting a 2-point conversion is p. a. Assume Temple will score two touchdowns and Killeen will not score. Create a decision tree for the decision of whether Temple's coach should go for a 1- point conversion or a 2-point conversion after each touchdown. The terminal nodes in the decision tree should be either WIN or LOSE for Temple. b. Assume that a WIN results in a value of 1.0 and LOSE results in a value of 0. Further, assume that the probability of converting a 2-point conversion is p = 28%. Should Temple's coach go for a 1-point conversion or 2-point conversion after scoring the first touchdown? 4. Question:Problem 1-15 (Algorithmic) Preliminary plans are underway for construction of a new stadium for a major league baseball team. City officials question the number and profitability of the luxury corporate boxes planned for the upper deck of the stadium. Corporations and selected individuals may purchase a box for $. The fixed construction cost for the upper-deck area is estimated to be $, with a variable cost of $ for each box constructed. a. What is the breakeven point for the number of luxury boxes in the new stadium? b. Preliminary drawings for the stadium show that space is available for the construction of up to 47 luxury boxes. Promoters indicate that buyers are available and that all 47 could be sold if constructed. What is your recommendation concerning the construction of luxury boxes? 5. Question:When production volume exceeds the breakeven point, we can expected 6. Question:A negative dual price indicates that increasing the right-hand side of the associated constraint would be detrimental to the objective. 7. Question:When the exponential distribution probability is given as P(x<9) = l-e -9 18 the average value for x is 8. Question:Because the dual price represents the improvement m the value of the optimal solution per unit increase in right-hand-side, a dual price cannot be negative 9. Question:Problem 2-11 (Algorithmic) Let A be an event that a person's primary method of transportation to and from work is an automobile and B be an event that a person's primary method of transportation to and from work is a bus. Suppose that in a large city P{A) = 0.46 and P{B} = 0.37. a. Are events A and B mutually exclusive? b. Find the probability that a person's primary method of transportation is some means other than a bus. If required, round your answer to two decimal places. 10. Question:If P(A U B) = P(A) + P(B), then A and B are mutually exclusive. 11. Question:A posterior probability associated with sample information is of the form 12. Question:One measure of the accuracy of a forecasting model is the 13. Question:The dual price for a < constraint 14. Question:In situations where you need to compare forecasting methods for different time periods, the most appropriate accuracy measure is 15. Question:Z is a standard normal random variable. What is the value of z if the area to the right of z is 0.9803? 16. Question:If A and B are mutually exclusive events, then P(A B) = 0. 17. Question:A cost that is incurred no matter what values the decision variables assume is 18. Question:P(AB) = P(B A) for all events A and B 19. Question:P(An B) 2 P(A) 20. Question:The decision variables of a model are also known as the 21. Question:An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is 22. Question:The improvement in the value of the objective function per unit increase in a right-hand side is the 23. Question:Whenever a categorical variable such as season has k levels, the number of dummy variables required 24. Question:Problem 7-37 (Algorithmic) The New England Cheese Company produces two cheese spreads by blending mild Cheddar cheese with extra sharp Cheddar cheese. The cheese spreads are packaged in 12-ounce containers, which are then sold to distributors throughout the Northeast. The Regular blend contains 75% mild Cheddar and 25% extra sharp, and the Zesty blend contains 70% mild Cheddar and 30% extra sharp. This year, a local dairy cooperative offered to provide up to 8 500 pounds of mild Cheddar cheese for $1.40 per pound and up to 2700 pounds of extra sharp Cheddar cheese for $1.60 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.40 per container. If each container of Regular is sold for $2.20 and each container of Zesty is sold for $2.00, how many containers of Regular and Zesty should New England Cheese produce? Do not round your interim computations. If required, round your answers to the nearest whole number. 25. Question:Problem 8-21 (Algorithmic) Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: a. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types b. How many reservations can be accommodated in each rental class? c. Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered? d. With a little work, an unused office area could be converted to a rental room. If the conversion cost is the same for both types of rooms, would you recommend converting the office to a Type I or a Type II room? 26. Question:e.Could the linear programming model be modified to plan for the allocation of rental demand for the next night? 27. Question:The complement of P(A | B) is 28. Question:Gradual shifting of a time series to relatively higher or lower values over a long period of time is called 29. Question:Which of the following exponential smoothing constant values puts the same weight on the most recent time series value as does a 5-period moving average? 30. Question:Problem 3-13 (Algorithmic) Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue the warning. Assume that a particular detection system has a 0.82 probability of detecting a missile attack. Answer the following questions using the binomial probability distribution: a. What is the probability that one detection system will detect an attack? If required, round your answer to two decimal places. b. If two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack? If required, round your answer to two decimal places. c. If 4 systems are installed, what is the probability that at least one of the systems will detect the attack? If required, round your answer to four decimal places. d. Would you recommend that multiple detection systems be operated?