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Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the  coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize  profit. Each roll of Grade X carpet uses 52 units of synthetic fiber, requires 28 hours of production time, and needs 22  units of foam backing. Each roll of Grade Y carpet uses 45 units of synthetic fiber, requires 30 hours of production time,  and needs 16 units of foam backing. The profit per roll of Grade X carpet is $205 and the profit per roll of Grade Y carpet is $155. In the coming production  period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800  hours of production time (overtime is a possibility.  This means that instead of using the = or ≤ sign in the constraint  you should use the ≥ sign.). The company has 1500 units of foam backing available for use. Develop and solve a linear programming model for this problem. :  Let X = the number of rolls of Grade X carpet to make Let Y = the number of rolls of Grade Y carpet to make What is the profit?

Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the  coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize  profit. Each roll of Grade X carpet uses 52 units of synthetic fiber, requires 28 hours of production time, and needs 22  units of foam backing. Each roll of Grade Y carpet uses 45 units of synthetic fiber, requires 30 hours of production time,  and needs 16 units of foam backing. The profit per roll of Grade X carpet is $205 and the profit per roll of Grade Y carpet is $155. In the coming production  period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800  hours of production time (overtime is a possibility.  This means that instead of using the = or ≤ sign in the constraint  you should use the ≥ sign.). The company has 1500 units of foam backing available for use. Develop and solve a linear programming model for this problem. :  Let X = the number of rolls of Grade X carpet to make Let Y = the number of rolls of Grade Y carpet to make What is the profit?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter3: Introduction To Optimization Modeling
Section: Chapter Questions
Problem 41P
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Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the 
coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize 
profit. Each roll of Grade X carpet uses 52 units of synthetic fiber, requires 28 hours of production time, and needs 22 
units of foam backing. Each roll of Grade Y carpet uses 45 units of synthetic fiber, requires 30 hours of production time, 
and needs 16 units of foam backing.
The profit per roll of Grade X carpet is $205 and the profit per roll of Grade Y carpet is $155. In the coming production 
period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 
hours of production time (overtime is a possibility.  This means that instead of using the = or ≤ sign in the constraint 
you should use the ≥ sign.). The company has 1500 units of foam backing available for use.
Develop and solve a linear programming model for this problem.
:  Let X = the number of rolls of Grade X carpet to make
Let Y = the number of rolls of Grade Y carpet to make
What is the profit?   

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