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 How much of each carpet X and carpet Y be produced to maximize profits?

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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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
How much of each carpet X and carpet Y be produced to maximize profits? 

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