Grand Canyon University BUS 660; Quantitative Methods For Business Midterm Exam: BUS 660 Midterm. Rated 85%

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BUS 660 Midterm 85% 1. When production volume exceeds the breakeven point, we can expected a profit 2. The complement of P(A | B) is P(AC | B) 3. If P(AU B) = P(A) + P(B), then A and B are mutua... lly exclusive. True 4. A negative dual price indicates that increasing the right-hand side of the associated constraint would be detrimental to the objective. True 5. 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? α = .2 6. When the exponential distribution probability is given as P(x ≤ 9 ) = 1 − e−9/18 the average value for x is 18 7. 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 $300000. The fixed construction cost for the upper-deck area is estimated to be $4500000, with a variable cost of $150000 for each box constructed. a. What is the breakeven point for the number of luxury boxes in the new stadium? Breakeven point 4,500,000/(300000-150000) = 4,350,000 Luxury Boxes b. Preliminary drawings for the stadium show that space is available for the construction of up to 50 luxury boxes. Promoters indicate that buyers are available and that all 50 could be sold if constructed. What is your recommendation concerning the construction of luxury boxes? 50(300000-150000)-45000007500000-4500000 3,000,000 Profit 8. Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side, a dual price cannot be negative. False 9. Gradual shifting of a time series to relatively higher or lower values over a long period of time is called trend. 10. If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation? 300x1 + 125x2 < 4,000 The variable{x_1}x1represents the number of ping pong balls produced per hour and variable{x_2}x2represents the number of wiffle balls produced per hour. A total of 300 ping pong balls are available and 125 wiffle balls are available. Hence, there is a constraint on the number of labor hours. Total labor hours taken by the ping pong balls will be 300{x_1}300x1and by wiffle balls will be125{x_2}125x2. Since a maximum of 4000 labor hours are available so 300{x_1} + 125{x_2} \ge 4000300x1+125x2≥4000is an incorrect constraint because it represents a minimum of 4000 total labor hours. The equation 425\left( {{x_1} + {x_2}} \right) \le 4000425(x1+x2)≤4000will not be a correct constraint because it does not includes the restriction on the total hours required by each ball. The equation 300{x_1} + 125{x_2} = 4000300x1+125x2=4000is a wrong constraint because according to this equation a total of 4000 labor hours are available but as per the provided study there are a maximum of 4000 labor hours. Total hours required to produce 300 ping pong balls \left( {{x_1}} \right)(x1) are 300{x_1}300x1and 125 wiffle balls \left( {{x_2}} \right) (x2)are125{x_2}125x2. Since maximum 4000 labor hours can be spent so the equation 300{x_1} + 125{x_2} \le 4000300x1+125x2 ≤4000is the correct constraint. The correct constraint is300{x_1} + 125{x_2} \le 4000300x1+125x2≤4000. 11. 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: Rental Class Room Super Saver Deluxe Business Type I $32 $43 — Type II $17 $35 $39 Type I rooms do not have wireless Internet access and are not available for the Business rental class.Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 120 rentals in the Super Saver class, 70 rentals in the Deluxe class, and 55 rentals in the Business class. Round Tree has 105 Type I rooms and 120 Type II rooms. 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. Variable # of reservations SuperSaver rentals allocated to room type I SuperSaver rentals allocated to room type II Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II Business rentals allocated to room type II b. Is the demand by any rental class not satisfied? Y/N Explain. The input in the box below will not be graded,but may be reviewed and considered by your instructor. c. How many reservations can be accommodated in each rental class? Rental Class # of reservations SuperSaver Deluxe Businessd. 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? e. 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? Why? The input in the box below will not be graded,but may be reviewed and considered by your instructor. f. Could the linear programming model be modified to plan for the allocation of rental demand for the next night? What information would be needed and how would the model change? The input in the box below will not be graded,but may be reviewed and considered by your instructor.12. The decision variables of a model are also known as the controllable inputs 13. A cost that is incurred no matter what values the decision variables assume is a sunk cost. 14. If A and B are mutually exclusive events, then P(A | B) = 0. True 15. Which of the methods for decision making best protects the decision maker from undesirable results? the conservative approach 16. An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is 16 17. The improvement in the value of the objective function per unit increase in a right-hand side is the dual price. 18. 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) = 0.48 and P(B) = 0.38. Are events A and B mutually exclusive? Yes What is the probability that a person uses an automobile or a bus in going to and from work? If required, round your answer to two decimal places. .48-.38 Yesa. 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. P(Bc) = =1-.38 19. 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 0.88 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. 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. 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.  Would you recommend that multiple detection systems be operated? [Show More]

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