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"Question 1 Preliminary plans are underway for the 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 buy the boxes for $100,000 each. The fixed construction cost for the upper-deck area is estimated to be $1,500,000, with a variable cost of $70,000 for each box constructed. What is the breakeven point for the number of luxury boxes in the new stadium? Choose one answer. A. 50 B. 30 C. 25 D. 75 Question 2 In the evaluation of a sales training program, a firm discovered that of 50 salespeople receiving a bonus last year, 15 had attended a special sales training program. The firm employs 250 sales people. Let B = the event that a salesperson makes a bonus and S = the event that a salesperson attends the sales training program. a) Find P(B), P(SB), and P (S n B). Choose one answer. A. 0.25, 0.40, 0.10 B. 0.20, 0.30, 0.06 C. 0.40, 0.10, 0.04 D. 0.10, 0.10, 0.01 Question 3 Please refer to Question 2. b) Assume that 60 % of the salespeople attended the training program. What is the probability that a salesperson makes a bonus given that the salesperson attended the sales training program, P(BS)? Choose one answer. A. 0.40 B. 0.36 C. 0.10 D. 0.28 Question 4 Solve the problem. Consider the given discrete probability distribution. Find P(x < 3). x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2 Choose one answer. A. .7 B. .2 C. .3 D. .5 Question 5 A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members regularly use each facility. A survey of the membership indicates that 65% regularly use the golf course, 49% regularly use the tennis courts, and 7% use neither of these facilities regularly. What is the probability that a worker regularly uses both golf and tennis facilities? Choose one answer. A. .49 B. .93 C. .21 D. .70 Question 6 The demand for a product of Carolina Industries varies greatly from month to month. Based on the past 2 years of data, the following probability distribution shows the company's monthly demand. Unit Demand Probability 300 0.10 400 0.35 500 0.35 600 0.20 a) If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina's monthly order quantity be for this product? Choose one answer. A. 377 B. 465 C. 570 D. 445 Question 7 Please refer to Question 6. Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $55. How much will the company gain or (lose) in a month if it places an order based on your answer to part (a) and the actual demand for the item is 420 units? Choose one answer. A. $5,875 B. ($1,250) C. $3,825 D. $1,675 Question 8 Please refer to Question 6. c) What are the variance and standart deviation for the number of units demanded? Choose one answer. A. 9475, 97.34 B. 8275, 90.97 C. 10345, 101.71 D. 9365, 96.77 Question 9 Suppose that you are given a decision situation with three possible states of nature: s1, s2, and s3. The prior probabilities are P(s1) = 0.40, P(s2) = 0.40, and P(s3) = 0.20. With sample information I, P(Is1) = 0.20, P(Is2) = 0.40, and P(Is3) = 0.05. Compute the revised or posterior probabilities: P(s1I), P(s2I), and P(s3I). Choose one answer. A. 0.32, 0.64, 0.04 B. 0.08, 0.16, 0.01 C. 0.30, 0.30, 0.40 D. 0.20, 0.20, 0.40 Question 10 In a certain state lottery, a lottery ticket costs $2. In terms of the decision to purchase or not to purchase a lottery ticket, suppose that the following payoff table applies. States of Nature Decision Alternatives Win s1 Lose s1 Purchase lottery ticket, d1 $300,000 -$2 Do not purchase lottery ticket, d2 0 0 A realistic estimate of the chances of winning are 1 in 150,000. What decision would you recommend based on the expected value approach? Choose one answer. A. d2 B. indifferent decisions C. d1 D. none Question 11 A new product has the following profit projections and associated probabilites. Profit Probability $120,000 0.10 $80,000 0.25 $40,000 0.20 0 0.15 -$75,000 0.20 -$150,000 0.10 What is the expected value? Should this new product be marketed? Choose one answer. A. -$10000; No B. $10,000; Yes C. -$30,000; No D. $30,000; Yes Question 12 Consider the following two-person, zero-sum game. Player B b1 b2 b3 Player A a1 2 1 4 a2 4 2 -5 a3 5 3 -2 What srategies can be dominated to reduce the game to a 2x2 game? Choose one answer. A. a1; b2 B. a2; b3 C. a2; b2 D. a3; b1 Question 13 Please refer to Question #12. Determine the optimal mixed strategy solution; what are p and q, respectively? Choose one answer. A. 0.63; 0.54 B. 0.45; 0.85 C. 0.78; 0.67 D. 0.75; 0.85 Question 14 The following data show the time series of the most recently quarterly capital expenditures (in billions of dollars) for the 1000 largest manufacturing firms: 18, 22, 25, 24, 23, 27, 29, 31, 29, 34, 37, and 39. What is the forecast one year (four quarters) into the future? Choose one answer. A. $39.1 billion B. $44.1 billion C. $42.6 billion D. $42.4 billion Question 15 A hotel chain collected the following data on the relationship between advertising and sales at a sample of six hotels. Advertising Expenditures ($1,000s) 1.0 3.0 6.0 10.0 14.0 Sales ($1,000s) 35 39 49 66 75 Let x represent advertising expenditures and y represent sales. What should the sales be for an advertising expenditure of $12,000? Choose one answer. A. $52,176 B. $65,263 C. $75,622 D. $69,733 Question 16 Solve the following linear program using the graphical solution procedure. Max 4A + 8B s.t. 2A <= 80 1B <= 60 2A + 2B <= 180 A, B => 0 What is the optimal solution? Choose one answer. A. A=70; B=40 B. A=60; B=80 C. A=35; B=75 D. A=30; B=60 Question 17 For the linear program Max 3A + 4B s.t -1A + 2B <= 8 1A + 2B => 12 2A + 1B <= 16 A, B => 0 What is the optimal solution? Choose one answer. A. A=6.667; B=1.667 B. A=4.800; B=6.400 C. A=5.867; B=2.667 D. A=6.143; B=2.234 Question 18 Marks: 5 Please refer to Question #17. What is the value of the objective function? Choose one answer. A. 35.687 B. 40.000 C. 28.550 D. 30.215 Question 19 Consider the following linear program Min A + 2B s.t 1A + 4B <= 21 2A + 1B => 7 3A + 1.5B <= 21 -2A + 6B => 0 A, B => 0 What is the optimal solution? Choose one answer. A. A=0; B=4 B. A=3; B=1 C. A=2; B=2 D. A=1; B=3 Question 20 Please refer to Question #19. What is the value of the objective function? Choose one answer. A. 3 B. 6 C. 5 D. 4

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