The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Decision Alternative d₁ d₂ States of Nature $₁ $2 $3 230 80 5 80 80 55 Suppose that the decision maker obtained the probabilities P(S₁) = 0.65, P(S₂) = 0.15, and P(S3) = 0.20. Use the expected value approach to determine the optimal decision. EV(d₁) = EV(d₂) =
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- Play Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters 15, 17, and 20. The current selling price is 45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters 5 million, 7.5 million, and 12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t 1) are determined as follows. Suppose that at the end of year t 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISKs output to find an interval such that you are 95% certain that the companys actual NPV will be within this interval.You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)
- W. L. Brown, a direct marketer of womens clothing, must determine how many telephone operators to schedule during each part of the day. W. L. Brown estimates that the number of phone calls received each hour of a typical eight-hour shift can be described by the probability distribution in the file P10_33.xlsx. Each operator can handle 15 calls per hour and costs the company 20 per hour. Each phone call that is not handled is assumed to cost the company 6 in lost profit. Considering the options of employing 6, 8, 10, 12, 14, or 16 operators, use simulation to determine the number of operators that minimizes the expected hourly cost (labor costs plus lost profits).The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. States of Nature Decision Alternative $1 52 53 d1 d2 240 90 15 90 90 65 Suppose that the decision maker obtained the probabilities P(s₁) = 0.65, P(s2) = 0.15, and P(S3) = 0.20. Use the expected value approach to determine the optimal decision. EV(d₁) EV(d2) = = The optimal decision is --?--✓The following payoff table shows a profit for a decision analysis problem with two decision alternatives and three states of nature. In order to get full credit, show your all work done step by step including cell calculations using excel functions. State of Nature Decion Alternatives s1 s2 s3 d1 250 100 50 d2 100 75 100 a) Construct a decision tree for this problem. b) Suppose that the decision-maker obtains the probabilities P(s1)=0.65, P(s2)=0.15, and P(s3)=0.20. Use the expected value approach to determine the optimal decision.
- The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Decision Alternative d₁ d₂ States of Nature 51 5₂ 53 260 110 35 110 110 85 The probabilities for the states of nature are P(S₁) = 0.65, P(S₂) = 0.15, and P(s) = 0.20. (a) What is the optimal decision strategy if perfect information were available? If s, then? ;If s₂ then 2 ✓; If s₂ then ? (b) What is the expected value for the decision strategy developed in part (a)? (c) Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? The recommended decision without perfect information is ? EV = (d) What is the expected value of perfect information? EVPI =The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): State of Nature Low Demand Medium Demand High Demand Decision Alternative s1 s2 s3 Manufacture, d1 -20 40 100 Purchase, d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. Use a decision tree to recommend a decision.Recommended decision: Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand. EVPI: $ fill in the blank 3 A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows: P(F | s1) = 0.10 P(U | s1) = 0.90 P(F | s2) = 0.40 P(U |…The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature: State of Nature Decision Alternative S1 S2 S3 di 150 100 25 d2 100 100 75 (a) Choose the correct decision tree for this problem. (i) (ii) S1 150 150 $2 2 100 di $3 100 25 83 d2 25 100 d2 $2 3 3 100 $3 S3 75 75 (iii) S1 (iv) 150 150 2 2 d2 100 100 100 100 S2 3 3 $2 100 100 d2 $3 di 25 25 $3 4 S3 75 75 |- Select your answer - v (b) If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? Optimistic approach Select your answer - v Conservative approach Select your answer - V Minimax regret approach - Select your answer
- A landlord can either lease for one or two years or sell offices outrightly for K100 million with payoffs as follows: Lease -100 50 150 Sell 100 100 100 The probability of rejecting is 30%, leasing for one year is 50% and for two years 20%. Required: What is the optimal decision strategy if perfect information were available? What is the expected value of perfect information? A decision maker is looking to minimising costs through three alternative decisions a1 , b2 and c3 under two states of nature/events S1 and S2 with S1 having a probability of 30% . For a1 payoffs for s1 K100 million and s2 K540 million For a2 payoff for s1 K150 million and s2 –K50 million For a3 payoff for s1 K350 million and s2 K320 million Required: Find EMV and recommend the course of action Find the…9. A decision-maker has two alternative courses of action, A1 and A2. There are three possible states of nature, S1, S2, and S3. The table of conditional profits, as well as the probabilities for the states of nature, appear below. Based on this decision table, which decision alternative produces the higher EMV? States of Nature Alternatives S1 S2 S3 A1 10,000 20,000 6,000 A2 5,000 30,000 15,000 Probability 0.3 0.5 0.2 Part 2 The best decision is ▼ a. alternative Upper A 1alternative A1 b. alternative Upper A 2alternative A2 , with an EMV=$________(enter your response as a whole number).The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): state of nature low demand medium demnad high demand Decision alternative s1 s2 s3 manufacture d1 -20 40 100 purchase d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. A test market study of the potential demand for the product is expected to report either a favourable (F) or unfavourable (U) condition. The relevant conditional probabilities are as follows: P(F|S1)=0.10 P (U|S1)=0.90 P(F|S2)=0.40 P (U|S2)=0.60 P(F|S3)=0.60 P (U|S3)=0.40 Decision tree leading to market study/ prediction of favorable…