A multinational corporation is considering the investment opportunities shown in the table below. TheBoard of Directors has specified the following:One of the two South American investment must be acceptedAt least two of the European investment must be acceptedNo more than one investment in Africa can be acceptedFurthermore, the corporation has only $40 million available to finance the investments. Formulate theproblem as an integer-programming problem.(i)(ii)(iii)Investment12345678LocationSouth AmericaSouth AmericaEuropeEuropeEuropeAfricaAfricaAfricaCost(in millions)$161210884616Expected profit(in millions)2.01.4$1.00.90.90.20.52.1

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Answered: A multinational corporation is…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 63P

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This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.
Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are 42.76, 81.33, and, 58.22, respectively. You plan to hold this portfolio for at least a year. During the coming year, economists have predicted that the national economy will be awful, stable, or great with probabilities 0.2, 0.5, and 0.3. Given the state of the economy, the returns (one-year percentage changes) of the three stocks are independent and normally distributed. However, the means and standard deviations of these returns depend on the state of the economy, as indicated in the file P11_23.xlsx. a. Use @RISK to simulate the value of the portfolio and the portfolio return in the next year. How likely is it that you will have a negative return? How likely is it that you will have a return of at least 25%? b. Suppose you had a crystal ball where you could predict the state of the economy with certainty. The stock returns would still be uncertain, but you would know whether your means and standard deviations come from row 6, 7, or 8 of the P11_23.xlsx file. If you learn, with certainty, that the economy is going to be great in the next year, run the appropriate simulation to answer the same questions as in part a. Repeat this if you learn that the economy is going to be awful. How do these results compare with those in part a?
Alexis Harrington received an inheritance of $95,000, and she is considering two speculative investmentsthe purchase of land and the purchase ofcattle. Each investment would be for 1 year. Under the present (normal) economic conditions, each dollar invested in land will return the principalplus 20% of the principal; each dollar invested in cattle will return the principal plus 30%. However, both investments are relatively risky. If economic conditions were to deteriorate, there is an 18% chance she would lose everything she invested in land and a 30% chance she would loseeverything she invested in cattle. Alexis does not want to lose more than $20,000 (on average). She wants to know how much to invest in eachalternative to maximize the cash value of the investments at the end of 1 year Should all of Alexis's inheritance be invested according to the optimal solution?
Alexis Harrington received an inheritance of $95,000, and she is considering two speculative investmentsthe purchase of land and the purchase ofcattle. Each investment would be for 1 year. Under the present (normal) economic conditions, each dollar invested in land will return the principalplus 20% of the principal; each dollar invested in cattle will return the principal plus 30%. However, both investments are relatively risky. If economic conditions were to deteriorate, there is an 18% chance she would lose everything she invested in land and a 30% chance she would loseeverything she invested in cattle. Alexis does not want to lose more than $20,000 (on average). She wants to know how much to invest in eachalternative to maximize the cash value of the investments at the end of 1 year How much "profit" would the optimal solution earn Alexis over and above her investment?
An investor is considering investing in stocks, real estate, or bonds economic conditions. Suppose that the probabilities for good, stable and poor conditions are 0.2, 0.4 and … (figure it out), respectively. Table 1 shows the payoff returns for the investor’s decision situation. Table 1: Investment returns Economic Conditions Investment Good Stable Poor Stocks R5 000 R7 000 R3 000 Real estate -R2 000 R10 000 R6 000 Bonds R4 000 R4 000 R4 000 Assuming the probabilities of the occurrence of the state of nature are unknown, what will be the best investment alternative; a) If the decision maker is pessimistic about the future state, (3) b) If the decision maker strikes a compromise between the maximin and maximax, assuming the coefficient of pessimism is 0.2. (4) c) If the decision is based on opportunistic loss. (6) d) If we use the equally likelihood criterion
A firm decides to invest x units of capital in project A and y units in project B. The expected return for 1 unit of investment is $400 in project A and $800 in project B. However, in order to meet the expectations of the firm’s ethical and environmental policy, the values of x and y must satisfy the constraintx2 + y2 − 4x − 6y = 67How many units of each type should the firm buy in order to maximize total return?
1. (i) A consumer has income of £3,000. Apple juice is priced at £3 a bottle and cheese is priced at £6 a kilo. Drawthe budget constraint for a consumer with standard preferences. What is the slope of this budget constraint? (ii) Show a consumer’s budget constraint and indifference curves for apple juice and cheese. Show the optimalconsumption choice. If the price of juice is £3 a bottle and the price of cheese is £6 a kilo, what is the marginalrate of substitution at this optimum? (iii) The price of cheese rises from £6 to £10 a kilo, while the price of juice remains at £3 a bottle. For aconsumer with a constant income of £3,000, show what happens to consumption of juice and cheese.Decompose the change into income and substitution effects.
Only Construct Linear Programming Model for the following Problemb; An individual wishes to invest $9000 over the next year in two typar of inventrent linvestment A yinlds 5% and invertment � yields 8%. Market retearch rocotnenends an allocs tion of at least 25% in A and at most 30% in �. Motsover, investment in A should be at least ball the invertmeut in �. How should the fund be allocated to the two imetrinents?
An investment advisor at RMC Financial Services wants to develop a model that can be used to allocate investment funds among four alternatives: stocks, bonds, mutual funds, and cash. For the coming investment period, the company developed estimates of the annual rate of return and the associated risk for each alternative. Risk is measured between 0 and 1, with higher risk value denoting more volatility and thus more uncertainty. The estimated rate of return for stocks is 10%, for bonds 3%, for mutual funds 4%, and cash 1%. The risk index for the stocks, bonds, and mutual funds investment is estimated as 0.8, 0.2, and 0.3, respectively. Because cash is held in money market funds, the annual return is lower, but it carries essentially no risk (i.e., risk index is zero for cash investment). The objective is to determine the portion of funds allocated to each investment alternatives in order to maximize the total annual return for the portfolio subject to the risk level the client is…
Vladimir Ulanowsky is playing Keith Smithson in atwo-game chess match. Winning a game scores 1 match 19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1029 point, and drawing a game scores 12match point. After thetwo games are played, the player with more match points isdeclared the champion. If the two players are tied after twogames, they continue playing until someone wins a game(the winner of that game will be the champion). Duringeach game, Ulanowsky can play one of two ways: boldly orconservatively. If he plays boldly, he has a 45% chance ofwinning the game and a 55% chance of losing the game. Ifhe plays conservatively, he has a 90% chance of drawing thegame and a 10% chance of losing the game. Ulanowsky’sgoal is to maximize his probability of winning the match.Use dynamic programming to help him accomplish thisgoal. If this problem is solved correctly, even thoughUlanowsky is the inferior player, his chance of winning the match is over 12. Explain this…
Which of the following is the converted constraint of 3x + 2y ≥ 35 under maximization of profit in simplex method? a. -3x +2y + S1 = -35 b. 3x +2y + S1 = 35 c. -3x -2y + S1 = -35 d. -3x -2y - S1 = -35 Which of the following is the converted constraint of 3x + 2y ≥ 35 under minimization of profit in simplex method? a. 3x + 2y - S1 + A1 = 35 b. 3x + 2y + S1 + A1 = 35 c. 3x + 2y + S1 - A1 = 35 d. 3x + 2y - S1 - A1 =-35 e. 3x + 2y - S1 + A1 =-35
An investor has a certain amount of money available to invest now. Three alternative investmentsare available. The estimated profit in Kwacha of each investment under each economic conditionare indicated in the following payoff table:Event Investment SelectionA B CEconomy declines 500 -2000 -7000No charge 1000 2000 -1000Economy Expand 2000 5000 20,000Based on his own past experience, the investor assigns the following probabilities to eacheconomic condition:( )( )( )Economy declines 0.30No change 0.50Economy expands 0.20PPP===i. Determine the optimal action based on the maximax criterion ii. Determine the optimal action based on the maximin criterion iii. Compute the expected monetary value (EMV) for each investment iv. Compute the expected opportunity loss (EOL) for each investment v. Explain the meaning of the expected value of perfect information (EVPI) in thisproblem vi. Based on the results of (iii) and (iv), which investment would you choose?vii. Compute the coefficient of…

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