The decision matrix shown consists of cost elements. Determine the alternative to be chosen using the following principles of choice: Laplace, minimax, minimin and Hurwicz with a = 0.4. Alternatives States of Nature S2 P36 S3 P24 S4 P17 A1 P25 A2 P40 P19 P28 Р36 A3 Р35 P21 P33 P27 A4 Р30 P29 P15 P23
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- 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.Suppose that a decision is faced with three decision alternatives and four states of nature.The following profit payoff table is constructed: ALTERNATIVES STATE OF NATURE S1 S2 S3 S4 A1 18 12 15 8 A2 15 14 10 11 A3 13 16 19 15 Assuming that the decision maker has no knowledge about the probabilities of occurrenceof the four states of nature, find the decisions to be recommended under each of thefollowing criteria:i. Maximin criterionii. Maximax criterioniii. Minimax Reject criterioniv. Hurwicz criterion with α = 0.6A payoff table is given as: S1 S2 S3 D1 250 750 500 D2 300 -250 1200 D3 500 500 600 (a) What choice should be made by the optimistic decision maker? (b) What choice should be made by the conservative decision maker? (c) What decision should be made under minimal regret? (d) If the probabilities of d1, d2, and d3 are .2, .5, and .3, respectively, then what choice should be made under expected value?
- 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?In the problem on excel : 1.What are the decision variables 2.What is the objective functions 3. What are the 12 constraints and explain You won $750,000 from a lottery and, you have decided to come up with a list of possible investments that you will invest, all of the $750,000 that you have won. The expected return of each of the 6 possible investments that you are considering investing in,and their Expected Rate of Return over the next year are in the table below. Investment Expected Rate of return Amazon Inc (USA Shares) 13.5% Royal Bank of Canada (Canadian Shares) 7.4% Nike Inc (USA Shares) 10.0% Telus Corporation (Canadian Shares) 6.1% Snap Inc (USA Shares) 3.0% Nestle SA (Switzerland Shares) 4.8% it is important to have a diversified portfolio, and therefore have come up with the following guidelines on how to invest your money: 1.The total invested in USA Shares should be at least 10% but no more then 45% of the total…Formulate the LP model for each of the problem identified below. Clearly define the decision variables and the objective function The Burroughs Garment Company manufactures men’s shirts and women’s blouses for Walmark Discount Stores. Walmark will accept all the products supplied by Burroughs. The production process includes cutting, sewing, and packaging. Burroughs employs 25 workers in the cutting department, 35 in the sewing department, and 5 in the packaging department. The factory works one 8-hr shift, 5 days a week. Determine the optimal weekly production schedule for Burroughs. The following table gives the time requirements and profits per unit for the two garments.
- 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 S2 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 Find EMV and recommend the course of action Find the EMV under certainty Use the EVC to find the EVPI Determine the opportunity loss table Find the course of action that minimises EOL Compare the minimum EOL with the EVPI.Which investment should Warren make under each of the following criteria? a. Maximax criterion. b. Maximin criterion. c. Maximum likelihood criterion. d. Bayes’ decision rule. e. The investor decides that Bayes’ decision rule is his most reliable decision criterion. He believes that 0.1 is just about right as the prior probability of an improving economy, but is quite uncertain about how to split the remaining probabilities between a stable economy and a worsening economy. Therefore, he now wishes to do some sort of sensitivity analysis with respect to these latter two prior probabilities. If he still wants to choose the alternative from the Bayes’ decision rule (part d): e1. How much would be the maximum amount of the prior probability of a stable economy? e2. How much would be the minimum amount of the prior probability of a worsening economy?A television network earns an average of $1.6 million each season from a hit program and loses an averageof $400,000 each season on a program that turns out to be a flop, and of all programs picked up by thisnetwork in recent years, 25% turn out to be hits and 75% turn out to be flops. a) Construct a decision tree to help the television network identify the strategy that maximizes itsexpected profit in responding to a newly proposed television program. Make sure to label all decisionand chance nodes and include appropriate costs, payoffs and probabilities. b) What should the network do? What is their expected profit? c) The network can conduct market research to determine whether a program will be a hit or a flop. Ifthe market research report is perfectly reliable, what is the most the network should be willing to payfor it? Can you please include pictures of excel sheets. Having trouble determining what the excel sheet should look like
- Wheels Distributors sells three types of tires to the commercial market. Type A. Type B and Type C. The anticipated payoffs are as follows for the three types of tires. Light Demand Moderate Demand Heavy Demand Probability 0.25 0.45 0.3 Tire Type A $325,000 $190,000 $170,000 B $300,000 $420,000 $400,000 C -$400,000 $240,000 $800,000 Construct a decision tree to help the management of Wheel Distributor make the appropriate decisions. This tree MUST be constructed in logical order with labels and net payoffs. Given the probabilities for the three types of tires and the expected monetary values, what decision should be made and what is that optimal expected value? What is the most should the firm be willing to pay to obtain further (perfect) information (EVPI) concerning the demand for the tires? 4. What decision should the firm…Zaki has been thinking about starting his own petrol station. He’s problem is to decide how large his petrol station should be. The annual return that will be achieved depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation: (Business Quantitative Analysis) Determine using the best investment using the following decision criteria: a) Maximax criterion b) Maximin criterion c) Equally Likely criterion d) Minimax Regret criterion The probabilities of good market, average market, and poor market are 0.4, 0.5, and 0.1 respectively. Construct an expected opportunity loss table. Using minimum EOL as the decision criterion, determine the best alternative1. Problem 13-14 (Algorithmic)The following profit payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:State of NatureDecision Alternative S1 S2 S3d1 200 150 75d2 250 150 50The probabilities for the states of nature are P(s1) = 0.5, P(s2) = 0.3 and P(s3) = 0.2.a. What is the optimal decision strategy if perfect information was available? S1 : d2 S2 : d1 or d2 S3 : d1 b. c. What is the expected value for the decision strategy developed in part (a)? If required, round your answer to one decimal place. d. Using the expected value approach, what is the recommended decision without perfect information? d2 What is its expected value? If required, round your answer to one decimal place. e. What is the expected value of perfect information? If required, round your answer to one decimal place.