A simple desicion-making model with maximalization criteria is given. State 1 State 2 State 3 State 4 Alternative1 20 30 10 15 Alternative2 30 10 40 20 Alternative3 15 15 20 15 p 0,4 0,3 0,2 0,1 Based on Maximax criterion we select Select one: the second alternative with profit 40 the first alternative with profit 30 the third alternative with profit 20

A simple desicion-making model with maximalization criteria is given. State 1 State 2 State 3 State 4 Alternative1 20 30 10 15 Alternative2 30 10 40 20 Alternative3 15 15 20 15 p 0,4 0,3 0,2 0,1 Based on Maximax criterion we select Select one: the second alternative with profit 40 the first alternative with profit 30 the third alternative with profit 20

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 40P

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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.)
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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 we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.
It has been suggested that at each iteration of the simplex algorithm, the entering variable should be (in a maximizationproblem) the variable that would bring about the greatest increase in the objective function. Although this usually results infewer pivots than the rule of entering the most negative row 0 entry, the greatest increase rule is hardly ever used. Why not?
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