The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives.Decision AlternativeState of Nature$1d₁d₂(a) Suppose P(s₁) = 0.2 and P(5₂) = 0.8. What is the best decision using the expected value approach?The best decision is --?--with an expected value of12$₂635(b) Perform sensitivity analysis on the payoffs for decision alternative d₂. Assume the probabilities are as given in part (a), and find the range of payoffs under states of natures, and so that will keep the solution found in part (a) optimal.As long as the payoff for s₁ under d₁ is --?--, then the solution found in part (a) will be optimal.then the solution found in part (a) will be optimal.As long as the payoff for s₂ under d₁ is --?--Is the solution more sensitive to the payoff under state of nature s₁ or 5₂?O $₁0 5₂

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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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
A 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 Decision Low Alternative Demand $1 Medium Demand $2 High Demand 53 Manufacture, d -5 55 115 Purchase, d₂ 60 85 The state-of-nature probabilities are P(s₁) = 0.35, P(52) = 0.35, and P(53) = 0.30. (a) Use a decision tree to recommend a decision. The best decision is to purchase the component part. (b) Use EVPI to determine whether the company should attempt to obtain a better estimate of demand, assuming the estimate would come at no further cost. EVPI = 9 The EVPI suggests that the company should consider an attempt to obtain a better estimate of demand. (c) A test market study of the potential demand for the product is expected to report either a favorable (F) or…
GENERATE THE DECISION VARIABLE SOLUTION AND GENERATE A SENSITIVITY REPORT CASE 1. Julia's Food Booth Julia Robertson is a senior at Tech, and she's investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia knows, from attending the games herself, that everyone eats a lot of food. She has to pay $1,000 per game for a booth, and the booths are not very large. Vendors can sell either food or drinks on Tech property, but not both. Only the Tech athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell. Most food items are sold during the hour before the game starts and during half time; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare…
A well-known plastic mould and die manufacturer in Toronto intends to expand internationally in anticipation of strong demand and expansion in the plastic die manufacturing sector. use the table beneath. Using the Maximax, Maximin, and equally likely conditions, assist the business in making the best option in an unclear situation. 0.5 for a highly favourable condition, 0.2 for an average demand, and 0.3 for an unfavourable state are the probabilities linked with the states of nature.a) Choose the course of action that will give Andrew the highest predicted monetary value (EMV).b) Determine the anticipated 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 |…
Aaron is considering potential
Imagine that you have the following pair of concurrent decisions. First examine both decisions, then indicate the options you prefer. Decision 1: Choose betweenA a sure loss of 1500B a 75% to lose £2000 and 25% chance to lose nothing Decision 2: Choose betweenC a sure gain of £480D a 25% chance to gain £2000 and 75% chance to gain nothing How do you think respondents in a laboratory experiment would decide in Decision 1 and Decision 2? most participants will choose 1B and 2C most participants will choose 1A most participants will choose 1B and 2D most participants will choose 1A and 2D 2) Which of the following can explain the behavior in the lab for decision 1? preference for certainty underestimation of large probabilities individuals are risk loving in the loss domain overweighting of small probabilities concavity of the value function in the gain domain 2. individuals are risk loving in the loss domain
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