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.

Chapter9: Decision Making Under Uncertainty

Section9.2: Elements Of Decision Analysis

Problem 2P

See similar textbooks

Similar questions

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.
7. Consider the following decision table, which Joe Blackburn has developed for Vanderbilt Enterprises: States of Nature Decision Alternatives Probability: 0.35 0.25 0.40 Low Medium High A $35 $80 $65 B $85 $50 $70 C $55 $70 $75 D $70 $85 $65 E $70 $75 $85 Part 2 The alternative that provides Blackburn the greatest expected monetary value (EMV LOADING... ) is ▼ D E A B C The EMV for this decision is $_______(enter your answer as a whole number).
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…
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): Decision State of Nature Alternative Low Demand (S1) Medium Demand (S2) High Demand )S3) Manufacture, d(1) -20 40 100 Purchase, d(2) 10 45 70 The state-of-nature probabilities are P s1= 0.35, P s2= 0.35, and P s3= 0.30 Use expected value to recommend a 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 following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. States of Nature Decision Alternative $1 52 53 d1 d2 240 90 15 90 90 65 Suppose that the decision maker obtained the probabilities P(s₁) = 0.65, P(s2) = 0.15, and P(S3) = 0.20. Use the expected value approach to determine the optimal decision. EV(d₁) EV(d2) = = The optimal decision is --?--✓
The following payoff table shows a profit for a decision analysis problem with two decision alternatives and three states of nature. In order to get full credit, show your all work done step by step including cell calculations using excel functions. State of Nature Decion Alternatives s1 s2 s3 d1 250 100 50 d2 100 75 100 a) Construct a decision tree for this problem. b) Suppose that the decision-maker obtains the probabilities P(s1)=0.65, P(s2)=0.15, and P(s3)=0.20. Use the expected value approach to determine the optimal decision.
9. A decision-maker has two alternative courses of action, A1 and A2. There are three possible states of nature, S1, S2, and S3. The table of conditional profits, as well as the probabilities for the states of nature, appear below. Based on this decision table, which decision alternative produces the higher EMV? States of Nature Alternatives S1 S2 S3 A1 10,000 20,000 6,000 A2 5,000 30,000 15,000 Probability 0.3 0.5 0.2 Part 2 The best decision is ▼ a. alternative Upper A 1alternative A1 b. alternative Upper A 2alternative A2 , with an EMV=$________(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 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 |…
An electronics factory operates on four production lines: laptops, mobiles, desktop computers, smart boards, and there were three cases of demand (weak, medium, and high), and the matrix of returns was as follows: Laptops Mobiles Risk Desktop Computers Smart Boards High 40 45 35 30 Economic state Medium 25 15 30 20 1. The problem presented above is decision-making under Certainty Uncertainty Weak 10 5 -10 -5 Save All Answers Save and Submit
What will be Hale’s TV Production’s decision based on the following criteria:a. MAXIMAXb. MAXIMINc. MINIMAX REGRETd. EXPECTED VALUEe. Construct the decision tree for this problem and indicate the decision based on the decision tree analysis.can you pls answer letter a,b,c
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…

SEE MORE QUESTIONS

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

SEE MORE TEXTBOOKS