Practical Management Science
5th Edition
ISBN: 9781305734845
Author: WINSTON
Publisher: Cengage
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Chapter 4.7, Problem 38P
Summary Introduction
To modify: The given model by making the changes and run the solver and interpret results.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
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Where a financial institution makes a loan commitment, the borrower, in drawing down on their loan commitment, causes increased cash flow needs by the DI to fund the loan commitments. There are three ways a DI can offset the effect of Asset-side liquidity risk such as drawing down of a loan commitment in all of the following sitiuations Except:
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Formulate but do not solve the problem.The management of a private investment club has a fund of $200,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low-risk. Management estimates that high-risk stocks will have a rate of return of 16%/year; medium-risk stocks, 8%/year; and low-risk stocks, 6%/year. The investment in low-risk stocks is to be twice the sum of the investments in stocks of the other two categories. If the investment goal is to have an average rate of return of 9%/year on the total investment, determine how much the club should invest in each type of stock. (Assume that all the money available for investment is invested. Let x, y, and z denote the amount, in dollars, invested in high-, medium-, and low-risk stocks, respectively.)
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The Schoch Museum (see Problem 30 in Chapter 11) is embarking on a five-year fundraising campaign. As a nonprofit institution, the museum finds it challenging to acquire new donors, as many donors do not contribute every year. Suppose that the museum has identified a pool of 8,000 potential donors. The actual number of donors in the first year of the campaign is estimated to be somewhere between 60% and 75% of this pool. For each subsequent year, the museum expects that a certain percentage of current donors will discontinue their contributions. This is expected to be between 10% and 60%, with a most likely value of 35%. In addition, the museum expects to attract some percentage of new donors. This is assumed to be between 5% and 40% of the current year’s donors, with a most likely value of 10%. The average contribution in the first year is assumed to be $50 and will increase at a rate between 0% and 8% each subsequent year, with the most likely increase of 2.5%. Develop and analyze a…
Chapter 4 Solutions
Practical Management Science
Ch. 4.2 - Prob. 1PCh. 4.2 - Prob. 2PCh. 4.2 - Prob. 3PCh. 4.2 - Prob. 4PCh. 4.2 - Prob. 5PCh. 4.2 - Prob. 6PCh. 4.3 - Prob. 7PCh. 4.3 - Prob. 8PCh. 4.3 - Prob. 9PCh. 4.3 - Prob. 10P
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- Suppose you begin year 1 with 5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 40% chance that the Whitewater stock will double, and there is a 60% chance that you will lose half of your investment. To illustrate, if the stock doubles during the first year, you will have 3750 under the mattress and 3750 invested in Whitewater during year 2. You want to estimate your annual return over a 30-year period. If you end with F dollars, your annual return is (F/5000)1/30 1. For example, if you end with 100,000, your annual return is 201/30 1 = 0.105, or 10.5%. Run 1000 replications of an appropriate simulation. Based on the results, you can be 95% certain that your annual return will be between which two values?arrow_forwardSuppose 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?arrow_forwardIn August of the current year, a car dealer is trying to determine how many cars of the next model year to order. Each car ordered in August costs 20,000. The demand for the dealers next year models has the probability distribution shown in the file P10_12.xlsx. Each car sells for 25,000. If demand for next years cars exceeds the number of cars ordered in August, the dealer must reorder at a cost of 22,000 per car. Excess cars can be disposed of at 17,000 per car. Use simulation to determine how many cars to order in August. For your optimal order quantity, find a 95% confidence interval for the expected profit.arrow_forward
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