Consider a game in which, simultaneously, player 1 selects a number x € [2, 8] and player 2 selects a number y E [2, 8]. The payoffs are given by: и, (х, у) —D 2ку -х2 и,(х, у) %—D 4ху — у?. Calculate the rationalizable strategy profiles for this game.
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- 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?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…Assume that $1,285,673 is to be invested in a project whose annual projected cash flows are as follows: Year 1 = $235,678, Year 2 = $267,854, Year 3 = $298,054, Year 4 = $314,567, and Year 5 = $325,678. Assume that the required rate of return is 5.25%. Compute the NPV by using Microsoft Excel's NPV function. Be sure to show your work. Should the project be pursued? Why or why not?
- Type the linear program, optimal solution, and objective function value in a word document. Submit your excel file. An investor wishes to invest some or all of his $12.5 million in a diversified portfolio through a commercial lender. The types of investments, the expected interest per year, and the maximum allowed percentage investment he will consider are shown on the following table. He wants at least 35% of his investments to be in nonmortgage instruments and no more than 60% to be in high-yield (and high-risk) instruments (i.e., expected interest > 8%). How should his investment be diversified to make the most interest income? Investment Expected Return Maximum Allowed Low-income mortgage loans 6.50% 20% Conventional mortgage loans 6.00% 30% Government sponsored mortgage loans 8.25% 25% Bond investments 5.75% 15% Stock investments 8.75% 18% Futures trading 9.25% 10%Assume that the Wisconsin Cheese Factory currently operates a large facility in Madison, WI. The owner, however, is concerned about concentration of risk and has decided to open up two new facilities to lessen that concentration, one in St. Cloud, MN, and the other in Iowa City, IA. Total production, while slightly less profitable overall because of additional operational costs, remains the same, with 1/3 at each location. This action is an example of _______. profit maximization loss reduction loss prevention risk avoidanceFormulate the situation as a system of inequalities. (Let x represent the number of dinghies the company can manufacture and y represent the number of rowboats.) A boat company manufactures aluminum dinghies and rowboats. The hours of metal work and painting needed for each are shown in the table, together with the hours of skilled labor available for each task. How many of each kind of boat can the company manufacture? (hours) Dinghy Rowboat Labor Available Metal Work 2 3 108 Painting 2 2 90 (labor for metal work) (labor for painting) x ≥ 0, y ≥ 0
- Perdaris Enterprises had an expenditure rate of E′(x) = e0.1x dollars per day and an income rate of I′(x) = 98.8 - e0.1x dollars per day on a particular job, where x was the number of days from the start of the job. The company’s profit on that job will equal total income less total expenditures. Profit will be maximized if the job ends at the optimum time, which is the point where the two curves meet. Find the following.(a) The optimum number of days for the job to last(b) The total income for the optimum number of days(c) The total expenditures for the optimum number of days(d) The maximum profit for the jobA company is considering a new product launch. There is a 0.6 chance thatdemand for the product will be strong and a 0.4 chance that demand will beweak. Two strategies for the launch are possible: 1 has high promotion costs anda net cash outflow of K120 000 if demand proves to be strong, and if demandproves weak a net cash outflow of (K30 000) will result. Strategy 2 has lowpromotion costs and if demand is strong will generate a cash inflow of only K80000 but with weak demand a net cash inflow of K20 000. i. Draw a decision tree and advise which course of action generates thegreatest expected profit. ii. What is the maximum amount that should be paid for market research todetermine with certainty whether demand will be strong or weak?What combination of x and y will yield the optimum for this problem? Maximize $10x + $4y, subject to (1) 5x + 3y ≤ 15 and (2) 3x + 6y ≤ 18 and (3) x, y ≥ 0.
- A small strip-mining coal company is trying to decide whether it should purchase or lease a new clamshell. If purchased, the “shell” will cost $152,500 and is expected to have a $50,000 salvage value after 6 years. Alternatively, the company can lease a clamshell for only $16,000 per year, but the lease payment will have to be made at the beginning of each year. If the clamshell is purchased, it will be leased to other strip-mining companies whenever possible, an activity that is expected to yield revenues of $9,000 per year. If the company’s MARR is 13% per year, should the clamshell be purchased or leased on the basis of a future worth analysis? Assume the annual M&O cost is the same for both options. The future worth when purchased is $ The future worth when leased is $A firm that plans to expand its product line must decide whether to build a small or a large facilityto produce the new products. If it builds a small facility and demand is low, the net present valueafter deducting for building costs will be $400,000. If demand is high, the firm can either maintainthe small facility or expand it. Expansion would have a net present value of $450,000, and maintaining the small facility would have a net present value of $50,000.If a large facility is built and demand is high, the estimated net present value is $800,000. If demandturns out to be low, the net present value will be – $10,000.The probability that demand will be high is estimated to be .60, and the probability of low demandis estimated to be .40.a. Analyze using a tree diagram.A firm that plans to expand its product line must decide whether to build a small or a large facilityto produce the new products. If it builds a small facility and demand is low, the net present valueafter deducting for building costs will be $400,000. If demand is high, the firm can either maintainthe small facility or expand it. Expansion would have a net present value of $450,000, and maintaining the small facility would have a net present value of $50,000.If a large facility is built and demand is high, the estimated net present value is $800,000. If demandturns out to be low, the net present value will be – $10,000.The probability that demand will be high is estimated to be .60, and the probability of low demandis estimated to be .40. 1- Compute the EVPI 2- Determine the range over which each alternative would be best in terms of the value of P ( low demand )