Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois,optical scanning firm:MaximizeZ= 1X₁ + 1x₂Subject to:2X₁ + 1X₂ ≤60(C₁)1X₁ + 2X₂ ≤60(C₂)X₁ X₂ 20On the graph on right, constraints C, and C₂ have been plotted.a) Using the point drawing tool, plot all the corner points for the feasible area.The optimum solution is:X₁ =(round your response to two decimal places).(round your response to two decimal places).X₂ =Optimal solution value Z =(round your response to two decimal places).b) If a technical breakthrough occurred that raised the profit per unit of X₁ to $3,due to this change, the optimal solutionAs a result of the technical breakthrough, the optimum solution is:X₁ =(round your response to two decimal places).X₂ =(round your response to two decimal places).Optimal solution value Z = (round your response to two decimal places).c) If the impact of technical breakthrough was incorrectly determined and insteadof X₁ profit coefficient increasing to $3 it only increases to $1.25. As a result ofthis correction, the optimal solution found originally

Given data is Objective function: Max Z=X1+X2 Subject to constraints: 1.) 2X1+1X2≤602.)…

Answered: Consider the following LP problem…

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 71P

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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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