Chapt 13

# Chapt 13 - Simulation 2 a Let c x = = variable cost per...

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Simulation 2. a. Let c = variable cost per unit x = demand Profit = 50 x - cx - 30,000 = (50 - c ) x - 30,000 b. Base case: Profit = (50 - 20) 1200 - 30,000 = 6,000 Worst case: Profit = (50 - 24) 300 - 30,000 = -22,200 Best case: Profit = (50 - 16) 2100 - 30,000 = 41,400 c. The possibility of a \$41,400 profit is interesting, but the worst case loss of \$22,200 is risky. Risk analysis would be helpful in evaluating the probability of a loss. 9. a. Base case using most likely completion times. A 6 B 5 C 14 D 8 33 weeks Worst case: 8 + 7 + 18 + 10 = 43 weeks Best case: 5 + 3 + 10 + 8 = 26 weeks b. Activity Random Number Completion Time A 0.1778 5 B 0.9617 7 C 0.6849 14 D 0.4503 8 Total: 34 Weeks c. Simulation will provide a distribution of project completion time values. Calculating the percentage of simulation trials with completion times of 35 weeks or less can be used to estimate the probability of meeting the completion time target of 35 weeks. 10. a. P (Win) = 18/38 = 0.4737 b. Win if RAND < 0.4737 c. Using random numbers in column 3, payoffs are in terms of money taken off the table. Payoff Payoff Win/Lose a b Win/Loss a b Win 25 0 Win 25 0 Lose -25 -50 Lose -25 -50 Win 25 0 Win 25 0 Win 25 75 Lose -25 -50 Lose -25 -25 Win 25 0 Win 25 0 Lose -25 -50 Lose -25 -50 Win 25 0

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Chapter 13 Lose -25 -25 Lose -25 -50 Win 25 0 Win 25 0 Lose -25 -50 Win 25 75 Strategy a \$ 50 Strategy b -\$250 Strategy a is the best and shows a winning of \$50 for the twenty bets. d. Note that the twenty simulations show 11 wins. This is a probability of winning of 11/20 = .55, which is more winning than can be expected in the long run. Longer simulation runs are needed to evaluate the two betting strategies. 14. The spreadsheet for this problem is as follows: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 A B C D E F G Madeira Manufacturing Company Selling Price per Unit \$50 Fixed Cost \$30,000 Variable Cost (Uniform Distribution) Demand (Normal distribution) Smallest Value \$16 Mean 1200 Largest Value \$24 Standard Deviation 300 Simulation Trials Variable Trial Cost per Unit Demand Profit 1 \$23.41 1179 \$1,338 2 \$19.95 1022 \$722 Note: To reconstruct the complete speadsheet: 1. Block rows 21 to 509 2. On the Insert menu, click Rows 3. Copy row 14 (Trial 2) to fill rows 15 to 510. Trial 500 will appear in row 512 of the spreadsheet. 499 \$16.36 1044 \$5,117 500 \$19.93 924 (\$2,209) Summary Statistics Mean Profit \$5,891 Standard Deviation \$9,439 Minimum Profit -\$24,013 Maximum Profit \$34,554 Number of Losses 129 Probability of Loss 0.2580 Selected cell formulas are as follows: Cell Formula B13 =\$C\$7+RAND()*(\$C\$8-\$C\$7) C13 =NORMINV(RAND(),\$G\$7,\$G\$8) D13 =(\$C\$3-B13)*C13-\$C\$4 a. The mean profit should be approximately \$6,000. Simulation results will vary with most
Simulation simulations having a mean profit between \$5,500 and \$6,500. b.

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Chapt 13 - Simulation 2 a Let c x = = variable cost per...

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