Answer questions $21-25$ based on the following information.

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 already been scheduled and must provide at least $1800$ hours of production time $($overtime is a possibility$).$ The company has $1500$ units of foam backing available for use.

You are asked to develop and solve a linear programming model for this problem.

First, define the decision variables. Select the proper definition of the decision variables for this problem.

$x=$ number of foam backing to purchase for Grade $x$ carpet

$Y=$ number of foam backing to purchase for Grade $Y$ carpet

$x=$ the profit for Grade $x$ carpet

$Y=$ the profit for Grade $Y$ carpet

$x=$ numbe of rolls of Grade $x$ carpet to make

$Y=$ number of rolls of Grade $Y$ carpet to make

$x=$ number of syntetic fiber to purchase for Grade $x$ carpet

$Y=$ number of syntetic fiber to purchase for Grade $Y$ carpet