Muir Manufacturing produces two popular grades of cornmercial carpeting among its many other products, In the coming production period, Muir needs to decide how many rolls of each Brade should be produced in order to maximize profit. Each roll of Grade Xcarpet uses $50$ units of synthetic fiber. requires $25$ hours of production time, and needs $20$ units of form backing. Each roll of Grade Y carpet uses $40$ units of synthetic fiber, requires $2\mathrm{.}8$ hours of production time, and needs $15$ units of foam backing:

The profit per roll of Grade $x$ eapet is $$200$ and the profit per roll af Grade $Y$ carpet is $5160.$ In the coming production period, Muir has $3000$ units of synthetic fiber available for use. Workers have already been scheduled and must provide ae least $1800/$zours of production time $($overtime is a possibility$).$ The company has $1500$ units of form backing available for use.

You are asked to develop and solve a lineac programming model for this probitem.

Firsti defenetie decision variablei. Select the proper definition of the decisfon veriables for this problem.