Data in the matrix below are COST in millions, determine which alternative is dominant using With and Without Probability (use a = .15 and probability of: 20%; 50% & 30% for S1, S2 and S3 respectively): Alternatives States of Nature Si S2 S3 D1 4.5 3 2 D2 2.5 4 D3 1 5 3
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- The probability distribution for the number of automobiles sold during a day (x) at Bob Iron Motors is as follows. x f(x) 0 0.001 1 0.007 2 0.034 3 0.099 4 0.188 5 6 0.220 7 0.136 8 0.055 9 0.015 10 0.001 21 The expected value of the number of automobiles sold is, a 5.20 b 5.31 c 5.42 d 5.53A bakery would like you to recommend how many loaves of its famous marble rye bread to bake at the beginning of the day. Each loaf costs the bakery $2.00 and can be sold for $7.00. Leftover loaves at the end of each day are donated to charity. Research has shown that the probabilities for demands of 25, 50, and 75 loaves are 30%, 20%, and 50%, respectively. Make a recommendation for the bakery to bake 25, 50, or 75 loaves each morning. Find the expected monetary value when baking 25 loaves. EMV=$(Type an integer or a decimal.) Find the expected monetary value when baking 50 loaves. EMV = $(Type an integer or a decimal.) Find the expected monetary value when baking 75 loaves. EMV = $ (Type an integer or a decimal.) Make a recommendation for the bakery to bake 25, 50, or 75 loaves each morning. The bakery should bake loaves of bread every morning. O 25 50 75 EA state government hired a contractor for a road construction project. The contractor's type, its cost efficiency, is known to the government. There is a 2/5 probability o its construction cost being 4 (billion dollars per lane) and 3/5 probability of the cost being 6. More lanes yield more social benefit in-the form of faster travel and fewer accidents. The social value V (measured in billions of dollars ) from having N lanes on the highway is V=15N-2N^2/3. The government is interested in option N and writing a contract to maximize the benefit of the state (V) net of the fee paid to the contractor (call it F) ; G=V-F. Your goal as a government official is to design a pair of contracts to separate the types of contractor. You want the contractor to choose (Contract L: Build N, lanes and get paid RL dollars" if its cost type is low cost of $4 billion dollars per lane and to choose "Contract H : Build NH lanes and get paid RH dollars" if its cost type is high cost $6 billion dollars per…
- 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 54 respectively): Which alternative is best using Expected Value? Alternatives S1 53 S4 A1 10 18 15 A2 12 25 20 A3 15 19 25 S2 20 15 18When small variations in a particular estimate would change which alternative is selected, the decision is said to be insensitive. O True O FalseIf the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 50,000 bushels. The cost of pesticides is $30,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $9.00 with probability of 0.50 or it will be $11.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $10.00. If the farmer decides to sell the crop at harvest, then: a. He should not use pesticides because not using pesticides ensures greater expected profit. b. He should not use pesticides because not using pesticides ensures lower expected profit. c. He should use pesticides because using pesticides ensures greater expected profit. d. He should use pesticides because using pesticides ensures lower expected profit.
- The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows: Procurement Cost($) 10 $ 11 12 Probability 0.25 0.45 0.30 Labor Cost ($) 20 22 24 25 Probability 0.10 0.25 0.35 0.30 Transportation Cost ($) 3 5 (a) Compute profit per unit for the base-case, worst-case, and best-case scenarios. Base Case using most likely costs Profit = $ /unit Worst Case Profit = $ /unit Best Case Profit = $ /unit Probability 0.75 0.25 (b) Construct a simulation model to estimate the mean profit per unit. (Use at least 1,000 trials.) (c) Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios? Simulation will provide ---Select--- of the profit per unit values which can then be used to find ---Select--- ◆ of an unacceptably low…EXAMPLE 18.3 Micro Pizza Heater: Market Demand A factory renovation is needed to build a compact microwave with a new shape, which will be called the Micro Pizza Heater. The low sales-volume prediction (20,000 heaters per year) has a subjectively estimated probability of 30%. The most likely market prediction is 30,000 units sold per year. The optimistic market prediction (30,000 sold the first year, with annual increases of 5000) has a subjectively estimated probability of 10%. In all cases, the factory equipment and the market will last 5 years. The net revenue will be $10 per microwave. What is the probability distribution for the net revenue?You are at a casino and there are three slot machines you can use to bet on. You must have a return of .5% of higher on what you are betting. Below is the expected returns for each slot machine under various scenarios. What combination of machines do you play to maximize your average return? Decision Variables Data Slot 1 100.0% Monday Tuesday Wednesda Average Slot 2 0.0% Slot #1 8% 4% 5% 5.667% Slot 3 0.0% Slot #2 2% -3% 3% 0.667% Slot #3 6% -2% 4% 2.667% Objective 5.7% Constraints 0.08 >= 0.5% 0.04 >= 0.5% 0.05 >= 0.5% 100.0% .: 100%
- The following table shows cost payoffs for four decision variables and four states of nature. S₁ S2 di 20 20 S S3 54 8 19 4 d2 12 12 40 d3 10 10 16 16 16 d4 30 30 25 20 20 9 110 14 14 Suppose the decision maker assigns the probability for S₁ = 0.10; S2 = 0.40; S3 = 0.20; and S4 = 0.30, what is the expected value of best decision? 21.2 21.8 20 19.2The 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. Use expected value to recommend a decision. b. Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.An individual has the following utility function u(w)=2w05 +10 using the expected utility, order the following prospects in terms of preference, from the most to the least preferred. P1 (0.9, 3,500, 500) P2 (0.7, 3700, 400) P3 (0.5, 5000, 350) What is the certainty equivalent level for P3.