Muir Manufacturing Produces Two Popular Grades of Commercial Carpeting Among

question 11

Essay

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 50 units of synthetic fiber,requires 25 hours of production time,and needs 20 units of foam backing.Each roll of Grade Y carpet uses 40 units of synthetic fiber,requires 28 hours of production time,and needs 15 units of foam backing.​
The profit per roll of Grade X carpet is $200,and the profit per roll of Grade Y carpet is $160.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).The company has 1500 units of foam backing available for use.​
Develop and solve a linear programming model for this problem.

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Definitions:

Simplify

The process of rendering an algebraic expression into its simplest form, making it easier to understand or solve.

Expression

A mix of numbers and symbols that signifies a math-based amount or connection.

X

Often used as a variable or unknown value in mathematics.

Expression

A combination of variables, numbers, and operations without an equal sign.