1. The following solved problems refer to this payoff table: New Bridge Built No New Bridge 14 Alternative capacity A 1 for new store B 10 4 where A small, B = medium, and C large. Assume the payoffs represent profits. Determine the alternative that would be chosen under each of these decision criteria: a. Maximin. b. Маximax. c. Laplace. 2. Using the information in the payoff table, develop a table of regrets, and then a. Determine the alternative that would be chosen under minimax regret. b. Determine the expected value of perfect information using the regret table, assuming that the probability of a new bridge being built is .60. 3. Using the probabilities of .60 for a new bridge and 40 for no new bridge, a. Compute the expected value of each alternative in the payoff table, and identify the alternative that would be selected under the expected-value approach. b. Construct a decision tree for the problem showing expected values.
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- Maximize z= 5R+8P Subject to R+3/2P≤900 1/2R+1/3P≤300 1/8R+1/4P≤100 R,P ≥ 0 non-binding constraint: R+(3/2) P≤900 binding constraints: (1/8) R+(1/4) P≤100 and (1/2) R+(1/3) P≤300 redundant constraint R+(3/2) P≤900 1. What is the range of the coeficient, c1, of the decision variable R that will make the optimal solution remain unchange? a. 13/3≤c1≤7 b. 10/3≤c1≤10 c. 4≤c1≤12 d. 13/2≤c1≤19/2 2. What is the range of the coeficient, c2, of the decision variable P that will make the optimal solution remain unchange? a. 13/3≤c1≤7 b. 10/3≤c1≤10 c. 4≤c1≤12 d. 13/2≤c1≤19/2Four proposals are being considered with investment and NPW shown below. C can only beconsidered if B is implemented. B and D and E are mutually exclusive. The budget is $80.A B C D EInvestment $10 $20 $30 $40 $50NPW $34 $28 $20 $16 $32a) Formulate this as a 0-1 integer program (objective function and constraints).b) Use trial and error to find all feasible solutions, and indicate which is optimal.c) Set up this problem in Excel, and use Solver to find the same optimal solutionConsider a small Oil production firm with 5 competing oil production projects, A - E. The table below shows the estimated long-term profit (Net Present Value) for each project as well as the amount of investment capital required to start the project. You have been contacted to help select the best combination of projects to maximize the Net Present Value subject to the capital investment limit of $32 million. Production Project A B C D E Estimated Profit (millions) 25 20 19 28 21 Capital Required (millions) 11 8 14 19 13 Formulate a Binary Integer Programming (BIP) model on a spreadsheet. Solver the model using Solver.
- 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.Given the following information for a product-mix problem with three products and three resources. Primal Decision Variables: x1 = number of unit 1 produced; x2 = # of unit 2 produced; x3 = # of unit 3 produced Primal Formulation:Dual Formulation: Max Z (Rev.) = 25x1 + 30x2 + 20x3Min W = 50π1+ 20π2+25π3 Subject To8x1+ 6x2+ x3≤ 50(Res. 1 constraint)Subject To8π1+ 4π2+2π3≥ 25 4x1+ 2x2+ 3x3≤ 20(Res. 2 constraint)6π1+ 2π2+π3 ≥ 30 2x1+ x2+ 2x3≤ 25(Res. 3 constraint)π1+ 3π2+2π3≥ 20 x1, x2, x3≥ 0 (Nonnegativity)π1, π2, π3 ≥ 0 Optimal Solution: Optimal Z = Revenue = $268.75 x1 = 0 (Number of unit 1)Dual Var. Optimal Value = 22.5 (Surplus variable in 1st dual constraint) x2 = 8.125 (Number of unit 2)Dual Var. Optimal Value = 0 (Surplus variable in 2nd dual constraint) x3 = 1.25 (Number of unit 3)Dual Var. Optimal Value = 0 (Surplus variable in 3rd dual constraint) Resource Constraints: Resource 1 = 0 leftover…Many decision problems have the following simplestructure. A decision maker has two possible decisions,1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utility.
- 1. 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.A food company is considering three different salad dressings to introduce nationally, Dressing A, B, and C. They also have the option to not introduce any dressing this year. The profits from dressings A, B, and C are $1,144,712, $1,515,938, and $2,525,542 respectively if the national market is favorable. However, if the national market is unfavorable, the losses are $555,615, $758,875, and $912,435 respectively. Historical data shows a probability of 0.568 for a favorable national market. The company can test the market for salad dressings in selected geographic areas before introducing them nationally. The cost of the test market is $53,331. In the past, the probability of a negative test market was 0.354. Given a positive test market, a favorable national market was actually observed with a probability of 0.745. Given a negative test market, a favorable national market was actually observed with a probability of 0.304. Determine if the company should test the market before…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 = 0.6
- 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…Suppose you have a choice of three projects to choose from. Here the expected profits from these projects under the following economic scenarios: Project Poor/Fair Moderate/Stable Strong/Booming A -200 $400 $700 B -700 600 1200 C 100 500 900 Now suppose the probability of a Poor/Fair economy is 25%, a Moderate/Stableeconomy is 45% and there is a 30% chance for a Strong/Booming economy.A) Setup a decision tree.B) Determine the expected value (EV) for each project. What project shouldbe selected based on the expected value approach? Why?C) Determine the expected value with perfect information about the states ofnature?D) Determine the expected value without perfect information about the states ofnature?E) Determine the expected value of perfect information.A company is considering a new product launch. There is a 0.6 chance that demand for the product will be strong and a 0.4 chance that demand will be weak. Two strategies for the launch are possible: 1 has high promotion costs and a net cash outflow of K120 000 if demand proves to be strong, and if demand proves weak a net cash outflow of (K30 000) will result. Strategy 2 has low promotion costs and if demand is strong will generate a cash inflow of only K80 000 but with weak demand a net cash inflow of K20 000. Draw a decision tree and advise which course of action generates the greatest expected profit. What is the maximum amount that should be paid for market research to determine with certainty whether demand will be strong or weak?