The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives.Decision AlternativeState of Nature51d₂d2(a) Use graphical sensitivity analysis to determine the range of probabilities of state of nature s, for which each of the decision alternatives has the largest expected value.d:is optimal for p(s₂) ≤ 0.2857; d. ✓ is optimal for p(s₂) > 0.28571252635(b) Suppose P(s) = 0.2 and P(5₂) = 0.8. What is the best decision using the expected value approach?The best decision is d:with an expected value of 5.2(c) Perform sensitivity analysis on the payoffs for decision alternative d₁. Assume the probabilities are as given in part (b), and find the range of payoffs under states of natures, and s₂ that will keep the solution found in part (b) optimal.As long as the payoff for s, is --?--, then d₂ will be optimal.As long as the payoff for s₂ is --?--Is the solution more sensitive to the payoff under state of nature s₁ or 5₂?0 5₁0 $₂Fthen d₂ will be optimal.

Given details:Decision AlternativeState of NatureS1S2d1123d265

Answered: The following payoff table shows the…

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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Very Favorable Average Market Unfavorable Alternatives Market Market Build new plant $250,000 $180.000 - S200,000 Subcontract $270.000 $185,000 - $220,000 Overtime S100.000 $50,000 - $12.000 Do Nothing SO SO $0 a) Using the decision making under uncertainty with the criterion of Maximax The appropriate decision will be The value of the return under this decision is $ b) Using the decision making under uncertainty with the criterion of Maximin The appropriate decision will be The value of the return under this decision is $ c) Using the decision making under uncertainty with the criterion of Equally Likely The appropriate decision will be The value of the return under this decision is $ (enter your answer as a whole number).
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.
Three decision makers have assessed utilities for the following decision problem (payoff in dollars). Decision Alternative 100 80 The indifference probabilities are as follows. 50 Payoff Decision Maker A 20 d₁ d₂ -20 -100 1.00 0.95 0.90 0.70 0.50 0.00 $1 $2 Decision Maker B should choose ?? 20 50 -20 Decision Maker C should choose ?? $3 80 100 -100 Decision Maker B 1.00 0.60 0.50 0.35 0.15 0.00 Decision Maker C 1.00 0.90 0.75 0.60 0.40 If P(S₁) = 0.25, P(S₂) = 0.50, and P(S3) = 0.25 and all decision makers assign a utility of 10 to the greatest payoff and a utility of 0 to the smallest payoff, find a recommended decision for each of the three decision makers. (Note: For the same decision problem, different utilities can lead to different decisions.) Decision Maker A should choose ?? ✓ 0.00
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 ? $1 240 90 90 15 The probabilities for the states of nature are P(S₁) = 0.65, P(s₂) = 0.15, and P(s3) = 0.20. (a) What is the optimal decision strategy if perfect information were available? ; If S₂ then ? 90 65 ; If S3 then ? (b) What is the expected value for the decision strategy developed in part (a)? î (c) Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? The recommended decision without perfect information is ? EV = (d) What is the expected value of perfect information? EVPI = î
Referring to the payoff table below answer the questions given below: State of Nature Decision Alternatives S1 S2 S2 S3 D1 7 4.5 5 2.5 D2 6 5 8 7 D3 4.5 5 5 5.5 D4 4 5 5.5 6.5 Construct decision tree for this problem Under the condition of uncertainty, what would be the recommended decision using the optimistic and pessimistic approaches?
1) A decision maker using an exponential utility function would prefer a random payoff with an expected value of X to a certain payoff of X. True False 2) In a decision tree, a circular node indicates a point where a random event occurs. True False 3) The optimistic and conservative approaches to decision making will always give the same result. True False
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Below pay-off was generated for your investment options. From this pay-off table determine the best decision using decision making under uncertainty: a.Maximax b.Maximin c.Minimax
A paint company has three sources for buying bright red pigment for its paints: Vietnam, Taiwan, and Thailand. Unfortunately, the pigment is made from a bush whose annual growth is heavily dependent upon the amount of rainfall during the growing season. The following tables show probabilities and prices for wet, dry, and normal growing seasons. Probabilities Wet Dry Normal Vietnam 0.5 0.2 Taiwan 0.6 0.3 Thailand 0.4 0.4 Price/Pound ($) Vietnam 0.96 1.11 Taiwan 0.86 1.25 Wet Dry Normal Thailand 0.92 1.19 0.3 What country shoul the company select? Thailand Taiwan Vietnam 0.1 0.2 1.05 0.99 1.06 What is the expected value (price) associated with it?
The University of Miami bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and preregistration records to determine how many copies of a text are needed. Preregistration shows 85 operations management students enrolled, but bookstore manager Vaidy Jayaraman has second thoughts, based on his intuition and some historical evidence. Vaidy believes that the distribution of sales may range from 65 to 85 units, according to the following probability model: Demand Probability 65 0.05 Stock 65 70 75 80 85 70 0.25 This textbook costs the bookstore $82 and sells for $107. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $30. a) Based on the given information, Vaidy's conditional profits table for the bookstore is: Demand 75 P=0.30 65 P = 0.05 0000 70 P = 0.25 75 0.30 ☐☐☐☐ 80 0.15 00000 80 85 P = 0.15 P = 0.25 30000 85 0.25 ☐☐☐☐
Problem 3 Picante Corporation expects demand for mp3 players that they produce to increase. Demand for their mp3 players for last year was as follows: MONTH JANUARY FEBRUARY MARCH APRIL 2,150 2,000 2,200 AUGUST SEPTEMBER OCTOBER 2,450 2,700 2,850 DEMAND 2,100 MONTH JULY DEMAND 2,650 MAY JUNE 2,500 2,350 NOVEMBER DECEMBER 3,150 3,000 a. Using least squares regression analysis, what would you estimate demand to be for each month next year? b. To be reasonably confident of meeting demand, Picante Corporation decides to use three standard errors of estimate for safety. How many additional units should be held to meet this level of confidence?
An oil company must decide whether or not to drill an oil well in a particular area that they already own. The decision maker (DM) believes that the area could be dry, reasonably good or a bonanza. See data in the table which shows the gross revenues for the oil well that is found. Decision Drill $0 Abandon $0 Probability 0.3 Dry (D) Seismic Results No structure(N) Open(0) Closed (C) Drilling costs 40M. The company can take a series of seismic soundings (at a cost of 12M) to determine the underlying geological structure. The results will be either "no structure", "open structure or "closed structure". The reliability of the testing company is as follows that is, this reflects their historical performance. Reasonably good(G) $85 $0 0.3 Note that if the test result is "no structure" the company can sell the land to a developer for 50 m. otherwise (for the other results) it can abandon the drilling idea at no benefit to itself. Dry(d) 0.7 0.2 Bonanza(B) 0.1 $200 m SO 0.4 Conditional…

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