Optimal Objective Value 2170.00000 Variable Value Reduced Cost АВ 100.00000 0.00000 BM 60.00000 0.00000 AP 0.00000 1.75000 BP 90.00000 0.00000 Constraint Slack/Surplus Dual Value 1 0.00000 12.25000 2 0.00000 9.00000 3 20.00000 0.00000 4 0.00000 -0.37500 Objective Allowable Allowable Variable Coefficient Increase Decrease AB 10.00000 1.75000 Infinite BM 6.00000 3.00000 2.33333 AP 14.00000 Infinite 1.75000 BP 9.00000 2.33333 3.00000 RHS Allowable Allowable Constraint Value Increase Decrease 1 100.00000 11.42857 100.00000 2 150.00000 Infinite 90.00000 3 600.00000 Infinite 20.00000 4 1080.00000 53.33333 480.00000

Optimal Objective Value 2170.00000 Variable Value Reduced Cost АВ 100.00000 0.00000 BM 60.00000 0.00000 AP 0.00000 1.75000 BP 90.00000 0.00000 Constraint Slack/Surplus Dual Value 1 0.00000 12.25000 2 0.00000 9.00000 3 20.00000 0.00000 4 0.00000 -0.37500 Objective Allowable Allowable Variable Coefficient Increase Decrease AB 10.00000 1.75000 Infinite BM 6.00000 3.00000 2.33333 AP 14.00000 Infinite 1.75000 BP 9.00000 2.33333 3.00000 RHS Allowable Allowable Constraint Value Increase Decrease 1 100.00000 11.42857 100.00000 2 150.00000 Infinite 90.00000 3 600.00000 Infinite 20.00000 4 1080.00000 53.33333 480.00000

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 67P

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Based on Grossman and Hart (1983). A salesperson for Fuller Brush has three options: (1) quit, (2) put forth a low level of effort, or (3) put forth a high level of effort. Suppose for simplicity that each salesperson will sell 0, 5000, or 50,000 worth of brushes. The probability of each sales amount depends on the effort level as described in the file P07_71.xlsx. If a salesperson is paid w dollars, he or she regards this as a benefit of w1/2 units. In addition, low effort costs the salesperson 0 benefit units, whereas high effort costs 50 benefit units. If a salesperson were to quit Fuller and work elsewhere, he or she could earn a benefit of 20 units. Fuller wants all salespeople to put forth a high level of effort. The question is how to minimize the cost of encouraging them to do so. The company cannot observe the level of effort put forth by a salesperson, but it can observe the size of his or her sales. Thus, the wage paid to the salesperson is completely determined by the size of the sale. This means that Fuller must determine w0, the wage paid for sales of 0; w5000, the wage paid for sales of 5000; and w50,000, the wage paid for sales of 50,000. These wages must be set so that the salespeople value the expected benefit from high effort more than quitting and more than low effort. Determine how to minimize the expected cost of ensuring that all salespeople put forth high effort. (This problem is an example of agency theory.)
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
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?
Bilbo Baggins wants to save money to meet threeobjectives. First, he would like to be able to retire 30 years from now with a retirementincome of $23,000 per month for 20 years, with the first payment received 30 yearsand 1 month from now. Second, he would like to purchase a cabin in Rivendell in10 years at an estimated cost of $320,000. Third, after he passes on at the end of the20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to hisnephew Frodo. He can afford to save $2,100 per month for the next 10 years. If hecan earn an 11 percent EAR before he retires and an 8 percent EAR after he retires,how much will he have to save each month in Years 11 through 30?
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SureStep is currently getting 160 regular-time hours from each worker per month. This is actually calculated from 8 hours per day times 20 days per month. For this, they are paid $9.375 per hour (51500y160). Suppose workers can change their contract so that they only have to work 7.5 hours per day regular-time— everything above this becomes overtime—and their regular-time wage rate increases to $10 per hour. They will still work 20 days per month. Will this change the optimal no-backlogging solution?
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Please no written by hand and no emage John is an investor. His portfolio primarily tracks the standard and poor 500 (S & P 500) and John wants to add the stock of ABC corp. Before adding the stock to his portfolio, he wants to assess the directional relationship between the stock and the S & P 500. John does not want to increase the unsystematic risk of his portfolio. Thus he is not interested in owning securities in the portfolio that tends to move in the same direction. The prices obtained are summarized in the table that follows:Required: Calculate the covariance of John’s stocks. State the implication of the outcome in project management decisions
We are considering investing in three stocks. The randomvariable Si represents the value one year from now of $1invested in stock i. We are given that E(S1) 1.15, E(S2) 1.21, E(S3) 1.09; var S1 0.09, var S2 0.04, var S3 0.01; cov(S1, S2) 0.006, cov(S1, S3) 0.004, and cov(S2,S3) 0.005. We have $100 to invest and want to have anexpected return of at least 15% during the next year.Formulate a QPP to find the portfolio of minimum variancethat attains an expected return of at least 15%.
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Suppose you are going to receive $20,000 per year forfive years. The appropriate interest rate is 7 percent.a. What is the present value of the payments if they are in the form of an ordinaryannuity? What is the present value if the payments are an annuity due?b. Suppose you plan to invest the payments for five years. What is the future valueif the payments are an ordinary annuity? What if the payments are an annuitydue?c. Which has the highest present value, the ordinary annuity or annuity due? Whichhas the highest future value? Will this always be true?