Archives: Solution Manual

1 2 3 4 17 18 19 20 21 22 23 24 25 Probabilities Number of Units Probability Cumulative Probability 0 0.2000 0.2000 1 0.1600 0.3600 2 0.1280 0.4880 3 0.1024 0.5904 4 0.0819 0.6723 5 0.0655 0.7379 14 15 16 31 32 33 34 35 36 37 38 39 11 0.0172 0.9313 12 0.0137 0.9450 13 0.0110 0.9560 14 0.0088 0.9648 15 0.0070 0.9719 16 0.0056 0.9775 17 0.0045 0.9820 18 0.0036 0.9856 19 0.0029 0.9885 26 27 28 29 30 A B C D E F G H I J Queuing Model M/M/s (Exponential Service Times) Probability (%

1 2 3 4 5 17 18 19 20 Probabilities Number of Units Probability Cumulative Probability 0 0.2500 0.2500 This system is now 4 independent M/M/1 queues with arrival rate = 12/4 = 3 per hour. Answers above are per queue. So multiply L and Lq by 4 to get system averages. (a) (3 customers) x (4 queues) = 12 customers total (b) 1.0 hour (c)

1 2 3 4 5 14 15 16 17 18 19 20 21 22 23 24 25 26 Probabilities Number of Units Probability Cumulative Probability 0 0.0377 0.0377 1 0.1132 0.1509 2 0.1698 0.3208 3 0.1698 0.4906 4 0.1274 0.6179 5 0.0955 0.7134 6 0.0716 0.7851 32 33 34 35 36 37 38 39 12 0.0128 0.9617 13 0.0096 0.9713 14 0.0072 0.9785 15 0.0054 0.9839 16 0.0040 0.9879 17 0.0030 0.9909 18 0.0023 0.9932 19 0.0017 0.9949 27 28 29 30 31 A B C D E F G H I J Problem 9-18 Queuing Model M/M/s (Exponential Service Times) 7

1 2 3 4 5 6 7 8 17 18 20 00.2500 0.2500 22 20.1406 0.5781 24 40.0791 0.7627 26 60.0445 0.8665 28 80.0250 0.9249 33 34 35 36 37 38 39 40 13 0.0059 0.9822 14 0.0045 0.9866 15 0.0033 0.9900 16 0.0025 0.9925 17 0.0019 0.9944 18 0.0014 0.9958 19 0.0011 0.9968 20 0.0008 0.9976 19 21 23 25 27 29 30 31 32 A B C D E F G H I J Queuing Model M/M/s (Exponential Service Times) Input Data Operating Characteristics Probabilities Number of Units Probability Cumulative Probability 10.1875 0.4375 30.1055 0.6836 50.0593 0.8220 70.0334 0.8999 90.0188 0.9437 10 0.0141 0.9578 11

1 2 3 4 5 14 15 16 17 18 19 20 21 22 23 24 25 26 Probabilities Number of Units Probability Cumulative Probability 0 0.1429 0.1429 1 0.1224 0.2653 2 0.1050 0.3703 3 0.0900 0.4602 4 0.0771 0.5373 5 0.0661 0.6034 6 0.0567 0.6601 32 33 34 35 36 37 38 39 12 0.0225 0.8652 13 0.0193 0.8845 14 0.0165 0.9010 15 0.0141 0.9151 16 0.0121 0.9272 17 0.0104 0.9376 18 0.0089 0.9465 19 0.0076 0.9542 27 28 29 30 31 A B C D E F G H I J Problem 9-16 Queuing Model M/M/s (Exponential Service Times) 7

1 2 3 4 5 6 7 8 9 15 16 17 18 31 32 33 34 35 36 37 38 39 11 0.0039 0.9923 12 0.0026 0.9949 13 0.0017 0.9966 14 0.0011 0.9977 15 0.0008 0.9985 16 0.0005 0.9990 17 0.0003 0.9993 18 0.0002 0.9995 19 0.0002 0.9997 21 22 23 24 25 26 1 0.2222 0.5556 0.4444 1+ 2 0.1481 0.7037 0.2963 2+ 3 0.0988 0.8025 0.1975 3+ 4 0.0658 0.8683 0.1317 5 0.0439 0.9122 0.0878 6 0.0293 0.9415 0.0585 19 20 27 28 29 30 A B C D E F G H I J Queuing Model

1 2 3 4 5 14 15 16 17 18 19 20 21 22 23 24 25 26 Probabilities Number of Units Probability Cumulative Probability 0 0.4286 0.4286 1 0.2449 0.6735 2 0.1399 0.8134 3 0.0800 0.8934 4 0.0457 0.9391 5 0.0261 0.9652 6 0.0149 0.9801 32 33 34 35 36 37 38 39 12 0.0005 0.9993 13 0.0003 0.9996 14 0.0002 0.9998 15 0.0001 0.9999 16 0.0001 0.9999 17 0.0000 1.0000 18 0.0000 1.0000 19 0.0000 1.0000 27 28 29 30 31 A B C D E F G H I J Problem 9-14 Queuing Model M/M/s (Exponential Service Times) 7

1 2 3 4 17 18 19 20 21 22 23 24 25 Probabilities Number of Units Probability Cumulative Probability 0 0.2000 0.2000 1 0.1600 0.3600 2 0.1280 0.4880 3 0.1024 0.5904 4 0.0819 0.6723 5 0.0655 0.7379 14 15 16 31 32 33 34 35 36 37 38 39 11 0.0172 0.9313 12 0.0137 0.9450 13 0.0110 0.9560 14 0.0088 0.9648 15 0.0070 0.9719 16 0.0056 0.9775 17 0.0045 0.9820 18 0.0036 0.9856 19 0.0029 0.9885 26 27 28 29 30 A B C D E F G H I J Problem 9-13 Queuing Model M/M/s (Exponential Service

1 2 3 4 5 14 15 16 17 18 19 20 21 22 23 24 25 26 Probabilities Number of Units Probability Cumulative Probability 0 0.6250 0.6250 1 0.2344 0.8594 2 0.0879 0.9473 3 0.0330 0.9802 4 0.0124 0.9926 5 0.0046 0.9972 6 0.0017 0.9990 32 33 34 35 36 37 38 39 12 0.0000 1.0000 13 0.0000 1.0000 14 0.0000 1.0000 15 0.0000 1.0000 16 0.0000 1.0000 17 0.0000 1.0000 18 0.0000 1.0000 19 0.0000 1.0000 27 28 29 30 31 A B C D E F G H I J Problem 9-12 Queuing Model M/M/s (Exponential Service Times) 7

1 2 3 4 5 14 15 16 17 18 19 20 21 22 23 24 25 26 Probabilities Number of Units Probability Cumulative Probability 0 0.1667 0.1667 1 0.1389 0.3056 2 0.1157 0.4213 3 0.0965 0.5177 4 0.0804 0.5981 5 0.0670 0.6651 6 0.0558 0.7209 32 33 34 35 36 37 38 39 12 0.0187 0.9065 13 0.0156 0.9221 14 0.0130 0.9351 15 0.0108 0.9459 16 0.0090 0.9549 17 0.0075 0.9624 18 0.0063 0.9687 19 0.0052 0.9739 27 28 29 30 31 A B C D E F G H I J Problem 9-11 Queuing Model M/M/s (Exponential Service Times) 7

Problem 9-10 1 2 3 4 Number of customers 300 300 300 300 Cost per waiting hour $13 $13 $13 $13 Number of checkout clerks Checkout clerk hourly salary $10 $10 $10 $10 Average waiting time per customer (minutes) 10 643 Total customer waiting time (hours) 50 30 20 15 Total waiting costs $650 $390 $260 $195 Total pay

1. Arrivals are FIFO. 3. Arrivals are independent. 5. Service times are independent. 2. Average time spent in the system (W) 4. Average time in the queue (Wq) 6. Percent idle time (Po) 9-4. If the service rate is not greater than the arrival rate (that is, μ < λ),

1 2 3 4 17 18 19 20 21 22 23 24 25 Probabilities Number of Units Probability Cumulative Probability 0 0.0016 0.0016 1 0.0095 0.0111 2 0.0285 0.0395 3 0.0569 0.0964 4 0.0854 0.1818 5 0.1024 0.2842 14 15 16 31 32 33 34 35 36 37 38 39 11 0.0473 0.7165 12 0.0406 0.7570 13 0.0348 0.7918 14 0.0298 0.8216 15 0.0255 0.8471 16 0.0219 0.8690 17 0.0187 0.8877 18 0.0161 0.9038 19 0.0138 0.9175 26 27 28 29 30 A B C D E F G H I J Queuing Model M/M/s (Exponential Service Times) Probability (%

current service times, even though a UPC reader is going to be installed. This means that our waiting times are an upper bound for the new, better system (the M/M/s model). We begin with a rough analysis (one that is going to have a very interesting feature, by the

1 2 3 4 17 18 19 20 21 22 23 24 25 Probabilities Number of Units Probability Cumulative Probability 0 0.1000 0.1000 1 0.0900 0.1900 2 0.0810 0.2710 3 0.0729 0.3439 4 0.0656 0.4095 5 0.0590 0.4686 14 15 16 31 32 33 34 35 36 37 38 39 11 0.0314 0.7176 12 0.0282 0.7458 13 0.0254 0.7712 14 0.0229 0.7941 15 0.0206 0.8147 16 0.0185 0.8332 17 0.0167 0.8499 18 0.0150 0.8649 19 0.0135 0.8784 26 27 28 29 30 A B C D E F G H I J Queuing Model M/M/s (Exponential Service Times) Probability (%

1 2 3 4 5 6 7 8 9 15 16 17 18 20 00.1765 0.1765 22 20.1729 0.5965 24 40.0847 0.8023 25 26 50.0593 0.8616 60.0415 0.9031 28 80.0203 0.9525 33 34 35 36 37 38 39 40 13 0.0034 0.9920 14 0.0024 0.9944 15 0.0017 0.9961 16 0.0012 0.9973 17 0.0008 0.9981 18 0.0006 0.9987 19 0.0004 0.9991 20 0.0003 0.9993 19 21 23 27 29 30 31 32 A B C D E F G H I J Queuing Model M/M/s (Exponential Service Times) Input Data Operating Characteristics Arrival rate (l)7Average server utilization (r)0.7000 Probabilities Number of Units Probability Cumulative Probability 10.2471 0.4235 30.1211

0.59 Good market (a) Conduct survey $60,000 If favorable, build large shop Large shop $60,000 $60,000 If unfavorable, don't build any shop 0.90 Good market $55,000 Large shop $60,000 $55,000 $0 $45,000 0.10 2Bad market $25,000 -$45,000 -$40,000 -$45,000 0.90 0.60 Good market Favorable $25,000 1Small shop $30,000 $25,000 $0 $45,000 $0 $21,000 0.10 Bad market -$15,000 -$10,000 -$15,000 No shop -$5,000 $0 -$5,000 Survey 0.12 -$5,000 $25,000 Good market $55,000 Large shop $60,000 $55,000 $0 -$33,000 0.88 Bad market -$45,000 -$40,000 -$45,000 0.12 0.40

Risk avoiders. -$45,000 -$40,000 -$5,000 $0 $95,000 $100,000 Monetary value Dollar Utility -$45,000 0.00 -$40,000 0.10 -$5,000 0.70 $100,000 1.00 Problem 8-27 (a) 0.60 Utility 0.20 0.00 0.40 0.80 1.00 Utility Curve $0 0.90 $95,000 0.99 0.82 High demand 0.55 Low demand Positive result 0.000 0.812 Not Construct 0.700 Study 0.761 High demand 0.109 0.89 20.000 0.900 0.700 0.50 High demand 0.900 0.550 0.50 Low demand No Study 0.100 20.100 0.812 0.18 10.000 0.700 0.11 0.990 Construct 0.990 0.45 Low demand Negative result 0.000 0.700 2 Not Construct 0.700 1.000 Construct 1.000 0.900 Not Construct 0.900 Problem 8-27 (b) Do not conduct study. 0.990 Do not construct

0.82 High demand (a) Construct clinic; EMV = $30,000 $95,000 (b) Conduct study. Construct clinic if positive result Construct $100,000 $95,000 Do not construct clinic if negative result. EMV = $36,140 $0 $69,800 0.18 (c) EVSI = $11,140 0.55 Low demand Construct $100,000 $100,000 $0 $30,000 0.50 Low demand No Study -$40,000 1 -$40,000 -$40,000 $0 $30,000 Not Construct $0 $0 $0 $95,000 Construct $100,000 $95,000 $0 -$29,600 0.89 0.45

TIME Alternatives None Mild Severe EMV Choice Broad 10 21 30 18.40 Worst outcome 10 20 20 Expected Value WITH Perfect Information (EVwPI) = 16.00 Expected Value OF Perfect Information (EVPI) = 0.60 Best Expected Time (EMV) = 16.60 REGRET Alternatives None Mild Severe EOL Choice Drexel 3 0 3 1.80 Best Expressway 10 4 0 5.60 Probability 0.40 0.40 0.20 In this

PAYOFFS Alternatives Good Fair Poor Maximum Choice Minimum Choice Average Choice Realism Choice Small $70,000 $28,000 -$14,000 $70,000 -$14,000 Best $28,000 $53,200 REGRET Alternatives Good Fair Poor Max regret Choice Small $350,000 $14,000 $0 $350,000 Medium $308,000 $0 $14,000 $308,000 Large $280,000 $0 $42,000 $280,000 Very large $0 $7,000 $210,000 $210,000 Best Problem 8-24 (c) Equally Likely (d) Hurwicz (e) Minimax Outcomes Outcomes (a) Maximax (b) Maximin Medium

Selling price $30.00 PAYOFFS Alternatives 50 100 150 200 EMV Choice 50 $500 $500 $500 $500 $500 100 -$300 $1,000 $1,000 $1,000 $740 Best 150 -$1,100 $200 $1,500 $1,500 $525 200 -$1,900 -$600 $700 $2,000 -$15 Probability 0.20 0.35 0.25 0.20 Best outcome $500 $1,000 $1,500 $2,000 Expected Value WITH Perfect Information (EVwPI) = $1,225 Best Expected Monetary Value (EMV) =

PAYOFFS Alternatives 50 100 150 200 Maximum Choice Minimum Choice Average Choice Realism Choice 50 $500 $500 $500 $500 $500 $500 Best $500 $500 100 -$300 $1,000 $1,000 $1,000 $1,000 -$300 $675 Best $610 150 -$1,100 $200 $1,500 $1,500 $1,500 -$1,100 $525 $720 200 -$1,900 -$600 $700 $2,000 $2,000 Best -$1,900 $50 $830 Best a = 0.7 REGRET Alternatives 50 100

Selling price $90.00 PAYOFFS Alternatives 6 7 8 9 EMV Choice 7$155 $245 $245 $245 $236 Best 8$100 $190 $280 $280 $217 9$45 $135 $225 $315 $171 Probability 0.10 0.50 0.30 0.10 6$210 $210 $210 $210 $210 Best outcome $210 $245 $280 $315 Best Expected Monetary Value (EMV) = $236 Expected Value OF Perfect Information (EVPI) = $23 Expected Value WITH Perfect

PAYOFFS Alternatives 100 300 500 EMV Choice 300 -$125 $375 $375 $175 Best 500 -$375 $125 $625 $50 Probability 0.40 0.35 0.25 Best outcome $125 $375 $625 100 $125 $125 $125 $125 Best Expected Monetary Value (EMV) = $175 Expected Value OF Perfect Information (EVPI) = $163 Expected Value WITH Perfect Information (EVwPI) = $338 REGRET Alternatives 100 300 500 EOL Choice 300

Selling price $2.50 a = 0.45 REGRET Alternatives 100 300 500 Maximum Choice 100 $0 $250 $500 $500 300 $250 $0 $250 $250 Best 500 $500 $250 $0 $500 (e) Minimax Problem 8-19 Demand Variable cost $1.25 PAYOFFS Alternatives 100 300 500 Maximum Choice Minimum Choice Average Choice Realism Choice 100 $125 $125 $125 $125 $125 Best $125 $125 Best 300 -$125 $375 $375 $375 -$125 $208

PAYOFFS Alternatives Grow Same Average Choice Realism Choice Large wing $225,000 -$125,000 $50,000 Best $120,000 Best (c) Hurwicz Problem 8-18 (b) Equally Likely Outcomes Small wing $90,000 -$65,000 $12,500 $43,500 No wing $0 $0 $0 $0 a = 0.7

PAYOFFS Alternatives Strong Average Weak EMV Choice Stocks 12% 6% -10% 0.00% Best Expected Monetary Value (EMV) = 3.25% Expected Value OF Perfect Information (EVPI) = 2.15% Expected Value WITH Perfect Information (EVwPI) = 5.40% REGRET Alternatives Strong Average Weak EOL Choice Bonds 5% 2% 1% 2.15% Best Money Market 8% 3% 0% 2.65% Probability 0.20 0.35 0.45 Stocks 0% 0% 12%

PAYOFFS Alternatives Strong Average Weak Maximum Choice Minimum Choice Average Choice Realism Choice REGRET Alternatives Strong Average Weak Maximum Choice Stocks 0% 0% 12% 12% Bonds 5% 2% 1% 5% Best Money Market 8% 3% 0% 8% (c) Equally Likely (d) Hurwicz Problem 8-16 Outcomes Outcomes Minimax (a) Maximax (b) Maximin Stocks 12% 6% -10% 12% Best -10% 3% 1% Bonds 7% 4% 1% 7% 1%

PAYOFFS Alternatives Good Average Poor EMV Choice Best outcome $90,000 $41,000 -$4,000 Best Expected Monetary Value (EMV) = $32,550 Expected Value OF Perfect Information (EVPI) = $7,200 Expected Value WITH Perfect Information (EVwPI) = $39,750 REGRET Alternatives Good Average Poor EOL Choice Move $0 $0 $24,000 $7,200 Best No change $50,000 $26,000 $0 $24,200 Probability 0.25 0.45 0.30 Expand $14,000 $11,000 $13,000

PAYOFFS Alternatives Good Average Poor Maximum Choice Minimum Choice Average Choice Realism Choice Expand $76,000 $30,000 -$17,000 $76,000 -$17,000 $29,667 $20,200 Best REGRET Alternatives Good Average Poor Maximum Choice Expand $14,000 $11,000 $21,000 $21,000 Best Move $0 $0 $32,000 $32,000 No change $50,000 $26,000 $0 $50,000 Outcomes (d) Hurwicz (e) Minimax Problem 8-14 (a) Maximax (b) Maximin (c) Equally Likely Outcomes Move $90,000 $41,000 -$28,000 $90,000 Best -$28,000 $34,333

PAYOFFS Alternatives Fav market Unfav market Maximum Choice Minimum Choice EMV Choice Acme $400,000 -$175,000 $400,000 Best -$175,000 $262,000 Best Problem 8-13 Outcomes (a) Maximax (b) Maximin (c) EMV Standard $280,000 -$90,000 $280,000 -$90,000 $191,200 High Pro $95,000 -$15,000 $95,000 -$15,000 Best $68,600 Probability 0.76 0.24

alternatives, (3) identify the possible outcomes, (4) evaluate the consequences, and (5) select an evaluation criterion and make the appropriate decision. The first four steps or procedures are common for all decision-making problems. Step 5, however, depends

0.15 0.25 Sales 130,000 $10,000 $260,000 $10,000 0.4 Sales 140,000 $30,000 Machine 1 $280,000 $30,000 (Semi-Automated) -$250,000 $21,450 Overtime 0.15 $38,000 Sales 150,000 $288,000 $38,000 1 $0 $38,000 Modify $35,000 $285,000 $35,000 Overtime 0.05 $46,000 Sales 160,000 $296,000 $46,000 2 $0 $55,000 2 Modify $26,300 $55,000 $305,000 $55,000 0.15 Sales 120,000 -$20,000 $330,000 -$20,000 0.25 Sales 130,000 $7,500 $357,500 $7,500 0.4 Machine 2 Sales 140,000 (Automated) $35,000 $385,000 $35,000 -$350,000 $26,300 0.15 Sales 150,000 $62,500 $412,500 $62,500 Overtime 0.05 $81,000 Sales 160,000 $431,000 $81,000 1 $0 $81,000 Modify $70,000 $420,000 $70,000 Internet Case: Toledo Leather Company Use automated machine. Sales 120,000 Expected profit = $26,300 -$10,000 $240,000 -$10,000

Cost per case (with overtime) = $1.50 + $1.75 + $0.90 = $4.15. Cost of machine = $350,000. Cost to modify machine = $20,000. Volume Profit (Excluding Cost of Machine) 120,000 ($6 – $3.25) × 120,000 = $330,000 130,000 ($6

PAYOFFS Alternatives Fav Mkt Unfav Mkt Max payoff Choice Min payoff Choice Do nothing $0 $0 $0.00 $0 Best a = 0.11 REGRET Alternatives Fav Mkt Unfav Mkt Max regret Choice Do nothing $210,000 $0 $210,000.00 Corp bonds $184,727 $10,000 $184,727.00 Pref stock $120,000 $15,000 $120,000.00 Com stock $0 $30,000 $30,000.00 Best Maximin Internet Case: Starting Right Outcomes Maximax Minimax Outcomes Corp bonds $25,273 -$10,000 $25,273.00 -$10,000 Pref stock

CHAPTER 8 DECISION ANALYSIS Internet Case Study: Starting Right This is an example of decision making under uncertainty. There are two outcomes: a favorable market and an unfavorable market (event 2). There are four alternatives: do nothing, invest in corporate bonds, invest in preferred stock, and invest

CHAPTER 8 DECISION ANALYSIS Internet Case Study: Ruth Jones’ Heart By-Pass Operation Expected survival rate with surgery = 0  0.05 + 1  0.45 + 5  0.20 + 10  0.13 + 15  0.08 + 20  0.05 + 25  0.04

0.8 0.6 Comp 12-months Moderate $100,000 $0 $95,000 $300,000 $100,000 0.3 Low 0.9 $50,000 Success (Continue) $250,000 $50,000 -$100,000 $154,000 0.1 Substantial $600,000 $800,000 $600,000 0.2 0.6 No comp 12-months Moderate 12-months normal $400,000 $0 $390,000 $600,000 $400,000 -$100,000 $128,600 0.3 Low $300,000 $500,000 $300,000 0.1 Failure (Stop) -$100,000 $0 -$100,000 0.6 Comp 8-months (Stop) -$80,000 $0 -$80,000 0.1 Substantial $160,000 $400,000 $160,000 0.8 0.6 Comp 12-months Moderate $60,000 $0 $55,000 $300,000 $60,000 8-months & crash 0.3 -$80,000 -$10,160 Low 0.9 $10,000 Success (Continue) $250,000 $10,000 -$160,000 $114,000 0.1 Substantial $560,000 $800,000 $560,000 0.2 0.6 0.4 No comp 12-months Moderate No comp 8-months $360,000 $0 $350,000 $600,000 $360,000 $0 $94,600 0.3 Low $260,000 $500,000 $260,000 0.1 Failure (Stop) -$80,000 $0 -$80,000 0.1 Substantial 1 $210,000 $128,600 $400,000 $210,000 0.5 0.6 Comp 6-months (Copy) Moderate $110,000 -$130,000 $105,000 $300,000 $110,000 0.3 Low $60,000 $250,000 $60,000 0.6 Comp 8-months (Stop) 6-months program -$80,000 $0 -$80,000 -$60,000 $47,420 0.1 Substantial $160,000 $400,000 $160,000 0.8 0.6 Comp 12-months Moderate $60,000 0.5 $0 $55,000 $300,000 $60,000 No comp 6-months 0.3 -$20,000 -$10,160 Low 0.9 $10,000 Success (Continue) $250,000 $10,000 -$160,000 $114,000 0.1 Substantial $560,000 $800,000 $560,000 0.2 0.6 0.4 No comp 12-months Moderate No comp 8-months $360,000 $0 $350,000 $600,000 $360,000 $0 $94,600 0.3 Low $260,000 $500,000 $260,000 0.1 Failure (Stop) -$80,000 $0 -$80,000 Do nothing $0 $0 $0 Internet Case: Drink At Home, Inc. 0.1 Adopt 12-month normal research program. Substantial Expected profit = $128,600 $200,000 $400,000 $200,000

CHAPTER 8 DECISION ANALYSIS Internet Case Study: Drink At Home, Inc. See file Ch08 Internet Case Drink At Home.XLS for the TreePlan solution. This is a fairly elaborate decision tree since we have to consider the possibility that competition may exist at the end of 6-months, 8-months.,

PAYOFFS Alternatives Poor Average Good Excellent EMV Choice PP -$5,000 -$2,000 $2,000 $5,000 $700 LB and PP -$10,000 -$4,000 $6,000 $12,000 $2,600 Best Outcomes Case: Ski Right TR and PP -$15,000 -$10,000 $7,000 $13,000 $900 CC and PP -$30,000 -$20,000 $10,000 $30,000 $1,000 LB, CC, and TR -$60,000 -$35,000 $20,000 $55,000 $2,500 Probability 0.1 0.3 0.4 0.2 Best outcome -$5,000 -$2,000

0.7 Succ venture 0.50 Unsucc venture Fav survey -$600,000 1 $0 -$600,000 $0 $800,000 No product -$100,000 $0 -$100,000 Hire MAI 0.4 -$100,000 $500,000 Succ venture $1,400,000 Introduce product $2,000,000 $1,400,000 -$500,000 $200,000 0.6 0.50 Unsucc venture Unfav survey -$600,000 1 $0 -$600,000 $0 $200,000 No product -$100,000 $0 -$100,000 Survey 1 0.87 $0 $500,000 Succ venture $1,200,000 Introduce product $2,000,000 $1,200,000 -$500,000 $940,000 0.13 0.62 Unsucc venture Fav survey -$800,000 1 $0 -$800,000 $0 $940,000 No product -$300,000 $0 -$300,000 Hire I&K 0.16 -$300,000 $468,800 Succ

Expressway -30 -30.0 2 0.5 -27.5 Congested -40 Broad street -40 -40 0 -27.5 0.5 Not congested -15 -15 -15 Use Broad street. Expected travel time = 27.5 minutes. Problem 8-50 (a) -30 Expressway 0.7 0.70 1 0.5 0.70 Congested 0.2 Broad street 0.2 0.2 0 0.55 0.5 Not congested 0.9 0.9 0.9 Use Expressway. Expected utility = 0.70. Problem 8-50 (b) 0.7 Time Utility 15 0.90 40 0.20 Risk avoider. Note: We have drawn the X-axis in reverse order so that

Conditional probabilities Prior probabilities P(Growth prediction | Actual growth) = 0.75 P(Actual growth) = 0.30 P(Growth prediction | Actual steady) = 0.18 P(Actual steady) = 0.45 Posterior probabilities GIVEN growth prediction Conditional prob Prior Joint Posterior Outcome P(Growth pred | Outcome) prob prob prob Actual growth 0.75 0.30 0.225 0.6955 Actual steady 0.18 0.45 0.081 0.2504 Actual

Conditional probabilities Prior probabilities P(Fav survey | Fav market) = 0.875 P(Fav mkt) = 0.550 Posterior probabilities GIVEN favorable survey Conditional prob Prior Joint Posterior Outcome P(Fav survey | Outcome) prob prob prob Fav market 0.875 0.550 0.481 0.855 Unfav market 0.182 0.450 0.082 0.145 P(Favorable survey) = 0.563 Posterior probabilities GIVEN unfavorable survey Conditional prob Prior Joint Posterior Outcome P(Unfav survey

Conditional probabilities Prior probabilities P(Favorable survey | Success) = 0.75 P(Sucess) = 0.50 P(Unfavorable survey | Success) = 0.25 P(Failure) = 0.50 Problem 8-47 P(Favorable survey | Failure) = 0.35 P(Unfavorable survey | Failure) = 0.65 Posterior probabilities GIVEN favorable survey Conditional prob Prior Joint Posterior Outcome P(Favorable | Outcome) prob prob prob Success 0.75 0.50 0.375 0.682 Failure 0.35 0.50 0.175 0.318 P(Favorable survey)

Conditional probabilities Prior probabilities P(Low survey | Low demand) = 0.70 P(Low demand) = 0.15 P(Fair survey | Low demand) = 0.20 P(Fair demand) = 0.40 P(High survey | Low demand) = 0.10 P(High demand) = 0.45 Fair demand 0.40 0.40 0.160 0.516 High demand 0.10 0.45 0.045 0.145 P(Low survey) = 0.310 Posterior probabilities GIVEN fair

Build 1.00 0.62 0.40 Failure No info 0.05 1 0.05 0.62 Not build 0.20 0.20 0.90 Success 0.40 Build 0.40 1 0.62 0.36 0.10 0.60 Failure Fav info 0.00 1 0.00 0.36 Not build 0.10 0.10 Get info 0.20 0.26 Success 0.40 Build 0.40 0.08 0.80 0.40 Failure Unfav info 0.00 2 0.00 0.10 Not build 0.10 0.10 Problem 8-45 (a) Get info. If favorable, build. 0.60 If unfavorable, don't build. Success Expected utility = 0.62. 1.00 Dollar Utility -$20,000 0.10 $0 0.20 $80,000 0.40 $100,000 1.00 0.75 Risk seeker. -$100,000 -$50,000 $0 $50,000 $100,000 Monetary value Problem

(a) Get info. If favorable, build. 0.6 If unfavorable, don't build. Success Expected return = $29,200. $100 0.9 Success $80 Build $100 $80 2 $29.20 $0 62 0.1 0.6 Failure Favorable -$100 1 -$80 -$100 $0 $62 Not build -$20 $0 -$20 Get info 0.2 -$20 $29.20 Success $80 Build $100 $80 $0 -64 0.8 0.4 Failure Unfavorable -$100 2 -$80 -$100 $0 -$20 Not build -$20 $0 -$20 Problem 8-44 (b) EVSI = $21.20 Build $100 $100 EVPI = $32.00 Efficiency

Lock-in now 0.150 Lock-in 1 month increases after one month, lock-in then. If rate is unchanged or decreases 0.100 0.100 and accept current rate at settlement. Expected utility = 0.300 0.500 Increase 0.5% Increase 0.5% 0.261. 1 0.000 0.100 0.000 0.250 Don't lock-in 1 month Unchanged 2 0.120 0.261 0.083 0.120 0.250 Decrease 0.5% 0.210 0.210 Lock-in 1 month 0.190 0.190 0.500 0.250 Don't lock-in now Unchanged Increase 0.5% 2 0.120 0.261 0.210 0.120 0.500 Don't