Use Sensitivity Information. If the right hand side of constraint 1 increases by 9 units, what answer characterizes the impact on the optimal solution? MIN 10X₁+6X₂ +14X3 +9X4S.T.1) 1x₁+1x3 1002) 1X₂+1X4-1503) 4X₁+3X₂<6004) 6X₁+8X₂<1080OPTIMAL SOLUTIONObjective Function Value =Variablex1Constraint12X2X3X4X2X3X4OBJECTIVE COEFFICIENT RANGESLower LimitVariablex1343Constraint12ليا عطرRIGHT HAND SIDE RANGES4Value100.00060.0000.00090.000slack/SurplusNo Lower Limit3.66712.2506.000Lower Limit0.00060.0002170.000580.000600.0000.0000.00020.0000.000Reduced Costs0.0000.0001.7500.000Dual Prices-12.250-9.0000.0000.375Current Value.10.0006.00014.0009.000Current Value100.000150.000600.0001080.000Upper Limit11.7509.000No Upper Limit11.333Upper Limit111.429No Upper LimitNo Upper Limit1133.333

Answered: Image /qna-images/answer/bd1416b6-5d3d-4bdd-8620-734ea6724c40.jpg

Answered: Use Sensitivity Information. If the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 78P

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You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).
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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