The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.States of NatureDecisionAlternative$15253d1d22409015909065Suppose 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 --?--✓

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Answered: The following payoff table shows profit…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section9.2: Elements Of Decision Analysis

Problem 2P

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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.
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).
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.
A common decision is whether a company should buy equipment and produce a product in house or outsource production to another company. If sales volume is high enough, then by producing in house, the savings on unit costs will cover the fixed cost of the equipment. Suppose a company must make such a decision for a four-year time horizon, given the following data. Use simulation to estimate the probability that producing in house is better than outsourcing. If the company outsources production, it will have to purchase the product from the manufacturer for 25 per unit. This unit cost will remain constant for the next four years. The company will sell the product for 42 per unit. This price will remain constant for the next four years. If the company produces the product in house, it must buy a 500,000 machine that is depreciated on a straight-line basis over four years, and its cost of production will be 9 per unit. This unit cost will remain constant for the next four years. The demand in year 1 has a worst case of 10,000 units, a most likely case of 14,000 units, and a best case of 16,000 units. The average annual growth in demand for years 2-4 has a worst case of 7%, a most likely case of 15%, and a best case of 20%. Whatever this annual growth is, it will be the same in each of the years. The tax rate is 35%. Cash flows are discounted at 8% per year.
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 51 230 80 $2 $3 80 5 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)
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. Decision Alternative d₁ d₂ States of Nature 51 52 $3 230 80 5 80 80 55 Suppose that the decision maker obtained the probabilities P(5₁) = 0.65, P(S₂) = 0.15, and P(53) = 0.20. Use the expected value approach to determine the optimal decision. EV(d₂) = EV(d₂) = The optimal decision is?.
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 $3 4 S3 75 75 |- Select your answer - v (b) If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? Optimistic approach Select your answer - v Conservative approach Select your answer - V Minimax regret approach - Select your answer
9. A decision-maker has two alternative courses of action, A1 and A2. There are three possible states of nature, S1, S2, and S3. The table of conditional profits, as well as the probabilities for the states of nature, appear below. Based on this decision table, which decision alternative produces the higher EMV? States of Nature Alternatives S1 S2 S3 A1 10,000 20,000 6,000 A2 5,000 30,000 15,000 Probability 0.3 0.5 0.2 Part 2 The best decision is ▼ a. alternative Upper A 1alternative A1 b. alternative Upper A 2alternative A2 , with an EMV=$________(enter your response as a whole number).
The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Decision Alternative If S1 d₁ d₂ States of Nature then ? $1 240 90 90 15 The probabilities for the states of nature are P(S₁) = 0.65, P(s₂) = 0.15, and P(s3) = 0.20. (a) What is the optimal decision strategy if perfect information were available? ; If S₂ then ? 90 65 ; If S3 then ? (b) What is the expected value for the decision strategy developed in part (a)? î (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 = î

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