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The PC Tech company assembles and then tests two models of computers, Basic and XP. For the coming month, the company wants to decide how many of each model to assemble and then test. No computers are in inventory from the previous month, and because these models are going to be changed after this month, the company doesn’t want to hold any inventory after this month. It believes the most it can sell this month are 600 Basics and 1200 XPs. Each Basic sells for $300 and each XP sells for $450. The cost of component parts for a Basic is $150; for an XP it is $225. Labor is required for assembly and testing. There are at most 10,000 assembly hours and 3000 testing hours available. Each labor hour for assembling costs $11 and each labor hour for testing costs $15. Each Basic requires five hours for assembling and one hour for testing, and each XP requires six hours for assembling and two hours for testing. PC Tech wants to know how many of each model it should produce (assemble and test) to maximize its net profit, but it cannot use more labor hours than are available, and it does not want to produce more than it can sell. As in the previous example, PC Tech must decide how many of each of its computer models to assemble and test, but there are now eight available models, not just two. Each computer must be assembled and then tested, but there are now two lines for testing. The first line tends to test faster, but its labor costs are slightly higher, and each line has a certain number of hours available for testing. Any computer can be tested on either line. The inputs for the model are same as before: (1) the hourly labor costs for assembling and testing, (2) the required labor hours for assembling and testing any computer model, (3) the cost of component parts for each model, (4) the selling prices for each model, (5) the maximum sales for each model, and (6) labor availabilities. These input values are listed in the file Product Mix 2.xlsx. As before, the company wants to determine the product mix that maximizes its total net profit. Use SolverTable to run a sensitivity analysis on the cost per assembling labor hour, letting it vary from $5 to $20 in increments of $1. Keep track of the computers produced in row 21, the hours used in the range B26:B28, and the total profit. Discuss your findings. Are they intuitively what you expected?

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Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

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Section
BuyFindarrow_forward

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
Chapter 3.7, Problem 12P
Textbook Problem
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The PC Tech company assembles and then tests two models of computers, Basic and XP. For the coming month, the company wants to decide how many of each model to assemble and then test. No computers are in inventory from the previous month, and because these models are going to be changed after this month, the company doesn’t want to hold any inventory after this month. It believes the most it can sell this month are 600 Basics and 1200 XPs. Each Basic sells for $300 and each XP sells for $450. The cost of component parts for a Basic is $150; for an XP it is $225. Labor is required for assembly and testing. There are at most 10,000 assembly hours and 3000 testing hours available. Each labor hour for assembling costs $11 and each labor hour for testing costs $15. Each Basic requires five hours for assembling and one hour for testing, and each XP requires six hours for assembling and two hours for testing. PC Tech wants to know how many of each model it should produce (assemble and test) to maximize its net profit, but it cannot use more labor hours than are available, and it does not want to produce more than it can sell.

As in the previous example, PC Tech must decide how many of each of its computer models to assemble and test, but there are now eight available models, not just two. Each computer must be assembled and then tested, but there are now two lines for testing. The first line tends to test faster, but its labor costs are slightly higher, and each line has a certain number of hours available for testing. Any computer can be tested on either line. The inputs for the model are same as before: (1) the hourly labor costs for assembling and testing, (2) the required labor hours for assembling and testing any computer model, (3) the cost of component parts for each model, (4) the selling prices for each model, (5) the maximum sales for each model, and (6) labor availabilities. These input values are listed in the file Product Mix 2.xlsx. As before, the company wants to determine the product mix that maximizes its total net profit.

Use SolverTable to run a sensitivity analysis on the cost per assembling labor hour, letting it vary from $5 to $20 in increments of $1. Keep track of the computers produced in row 21, the hours used in the range B26:B28, and the total profit. Discuss your findings. Are they intuitively what you expected?

Summary Introduction

To track: The computers produced in row 21 by varying the cost per assembling labor hour from $5 to $20 in increment of $1.

Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints, then it is said to be an unfeasible solution.

Explanation of Solution

Compute net profit using the given information:

Figure (1)

Solving parameters are given as follows:

Figure (2)

Track the computers produced in row 21 by varying the cost per assembling labor hour from $5 to $20 in increment of $1:

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Chapter 3 Solutions

Practical Management Science
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Ch. 3.7 - The PC Tech company assembles and then tests two...Ch. 3.7 - The PC Tech company assembles and then tests two...Ch. 3.7 - The PC Tech company assembles and then tests two...Ch. 3.7 - The PC Tech company assembles and then tests two...Ch. 3.7 - The PC Tech company assembles and then tests two...Ch. 3.7 - The PC Tech company assembles and then tests two...Ch. 3.7 - The PC Tech company assembles and then tests two...Ch. 3.8 - The Pigskin Company produces footballs. Pigskin...Ch. 3.8 - The Pigskin Company produces footballs. Pigskin...Ch. 3.8 - The Pigskin Company produces footballs. Pigskin...Ch. 3.8 - In one modification of the Pigskin problem, the...Ch. 3.8 - Modify the Pigskin spreadsheet model so that...Ch. 3.8 - Modify the Pigskin spreadsheet model so that...Ch. 3.8 - Modify the Pigskin spreadsheet model in the...Ch. 3 - A chemical company manufactures three chemicals:...Ch. 3 - A furniture company manufactures desks and chairs....Ch. 3 - A farmer owns 450 acres of land. He is going to...Ch. 3 - During the next four months, a customer requires,...Ch. 3 - A company faces the following demands during the...Ch. 3 - Maggie Stewart loves desserts, but due to weight...Ch. 3 - For a telephone survey, a marketing research group...Ch. 3 - A furniture company manufactures tables and...Ch. 3 - A manufacturing company makes two products. Each...Ch. 3 - There are three factories on the Momiss River....Ch. 3 - A company manufactures two types of trucks. Each...Ch. 3 - A company manufactures mechanical heart valves...Ch. 3 - A company that builds sailboats wants to determine...Ch. 3 - A company manufactures two products on two...Ch. 3 - A textile company produces shirts and pants. Each...Ch. 3 - Each year, a shoe manufacturing company faces...Ch. 3 - A small appliance manufacturer must meet (on time)...Ch. 3 - A pharmaceutical company manufactures two drugs at...Ch. 3 - In any optimization model such as those in this...Ch. 3 - Suppose you use Solver to find the optimal...Ch. 3 - Consider an optimization model with a number of...Ch. 3 - If you add a constraint to an optimization model,...Ch. 3 - Why is it generally necessary to add nonnegativity...Ch. 3 - Suppose you have a linear optimization model where...Ch. 3 - In a typical product mix model, where a company...Ch. 3 - In a typical product mix model, where a company...Ch. 3 - In a typical production scheduling model like...Ch. 3 - In a production scheduling problem like Pigskins,...Ch. 3 - Shelby Shelving is a small company that...

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