Data in the matrix below indicates COST expected from 3 alternatives under 4 states of nature. Determine which alternative is dominant using With and Without Probability (use a = 0.3 and probability of: 30%, ; 20%; 40% & 10% for S1, S2, S3, and S4 respectively): Alternatives si S2 S3 S4 A1 10 20 18 15 A2 12 15 25 20 АЗ 15 18 19 25
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- 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 A.Compute the probabilities by completing the table Sate of…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 What is the expected value of the market research information?…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 A.Compute the probabilities by completing the table Sate of…
- The owner of a ski resort is considering installing a new ski lift that will cost $900,000. Expenses for operating andmaintaining the lift are estimated to be $1,500 per day when operating. The U.S. Weather Service estimates thatthere is a 60% probability of 80 days of skiing weather per year, a 30% probability of 100 days per year, and a 10% probability of 120 days per year. The operators of the resort estimate that during the first 80 days of adequate snow in a season, an average of 500 people will use the lift each day, at a fee of $10 each. If 20 additional days are available, the lift will be used by only 400 people per day during the extra period; and if 20 more days of skiing are available, only 300 people per day will use the lift during those days. The owners wish to recover any invested capital within five years and want at least a 25% per year rate of return before taxes. Based on a before-tax analysis, should the lift be installed?Which decision rule is most concerned with downside risk? A) Expected monetary value B) Maximax C) Maximin D) None of the aboveWe consider the following decision problem, with 4 decisions di,i∈{1,…,4}, and four possible outcomes ωi,i∈{1,…,4}, with the following table of profits: ω1 ω2 ω3 ω4 d1 30 30 0 30 d2 20 20 20 20 d3 0 50 10 40 d4 15 30 10 25 Which decision should be chosen for rewards depending on four different possible outcomes, according to the maximin rule, maximax rule, and optimism-pessimism rule with α<1/3?
- Suppose that the point spread for a particular sporting event is 10 points and that with this spread you are convinced you would have a 0.60 probability of winning a bet on your team. However, the local bookie will accept only a $1000 bet. Assuming that such bets are legal, would you bet on your team? (Disregard any commission charged by the bookie.) Remember that you must pay losses out of your own pocket. Your payoff table is as follows: STATE OF NATURE DECISION ALTERNATIVES YOU WIN YOU LOSE BET $1000 -$1000 DON’T BET $0 $0 What decision does the expected value approach recommend? What is your indifference probability for the $0 payoff? (Although this choice isn't easy, be as realistic as possible. It is required for an analysis that reflects your attitude toward risk.) What decision would you make based on the expected utility approach? In this case are you a risk taker or a risk avoider? Would other individuals assess the same…Market Data Rate of Return Standard Deviation Treasury Bills 4.25% 0.00% S&P 500 12.00% 21.00% Required: Using the information in the table above and the varying risk aversions below, please calculate allocations to the risky and risk-free assets. (Use cells A5 to C6 from the given information to complete this question.) Risk Aversion Percent Allocated to the Market (S&P 500) Percent Allocated to Treasury Bills 4.00 2.00 1.50only a,b,c,or d option no explanation Three applicants are to be selected at random out of 4 boys and 6 girls. What is the probability of selecting, at least one girl? Answer Answer Option a) 0.5 b) 0.15 d) 0.366 c) 0.636
- a. If the decision maker knows nothing about the probabilities of the fourstates of nature, what is the recommended decision using:i. the optimistic approachii. the conservative approachiii. the minimax regret approachiv. the Laplace method2.4.1 Total Cost in Material SelectionIn many cases, economic selection among materials cannot be based solely on the costs ofmaterials. Frequently, a change in materials will affect the design and processing costs, and shipping costsmay also be altered.Care should be taken in making economic selections between materials to ensure that anydifferences in shipping costs, yields, or resulting scrap are taken into account. Commonly, alternativematerials do not come in the same stock sizes, such as sheet sizes and bar lengths. This may considerablyaffect the yield obtained from a given weight of material. Similarly, the resulting scrap may differ forvarious materials.In addition to deciding what material a product should be made of, there are often alternativemethods or machines that can be used to produce the product, which, in turn, can impact processingcosts. What could be the factors affecting the cost of materials that one should consider?I am in possession of two coins. One is fair so that it lands heads (H) and tails (T)with equal probability while the other coin is weighted so that it always lands H. Bothcoins are magical: if either is flipped and lands H then a $1 bill appears in your wallet,but when it lands T nothing happens. You may only flip a coin once per period. Theinterest rate is i per period. You are risk-neutral and thus only concern yourself withexpected values (and not variance). For simplicity, in the questions below assumeyou will live forever.1. How much are you willing to pay for such a coin that you know is fair? 2. How much are you willing to pay for such a coin that you know is weighted? 3. I currently own the coins and know which is fair and which is weighted, but youcannot tell which is which. You may make an offer to purchase a coin of yourchoosing, which I am free to accept or reject. What is the most you are willingto offer? Explain how you arrived at this answer.