Consider the following linear program.Max 3A + 2Bs.t.1A1B ≤ 103A + 1B ≤ 221A + 2B ≤ 18A, B ≥ 0(a) Use the graphical solution procedure to find the optimal solution.What is the value of the objective function at the optimal solution?at (A, B) =(b) Assume that the objective function coefficient for A changes from 3 to 5. Use the graphical solution procedure to find the new optimal solution.Does the optimal solution change?The extreme point(c) Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Use the graphical solution procedure tofind the new optimal solution.Does the optimal solution change?The extreme pointVariable(d) The computer solution for the linear program in part (a) provides the following objective coefficient range information.Objective Allowable AllowableCoefficient Increase DecreaseAB---Select--- optimal. The value of the objective function becomes3.000002.00000---Select--- optimal. The value of the objective function becomes3.000001.000001.000001.00000 Use this objective coefficient range information to answer parts (b) and (c).The objective coefficient range for variable A isto---Select--- change. The objective coefficient range for variable B isoptimal solution ---Select--- ✓ change.Since the change in part (b) is ---Select--- this range, we know the optimal solutionSince the change in part (c) is ---Select--- this range, we know theto

As per Bartleby guidelines, we can only solve the first three subparts of one question at a…

Answered: (a) Use the graphical solution…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 51P

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Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?
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.

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