Solve the following:
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 30 hours of production time, and needs 15 units of foam backing.
The profit per roll of Grade X carpet is $180 and the profit per roll of Grade Y carpet is $150. In the coming production period, Muir has 3000 units of synthetic fiber available for use. There is 1800 hours of production time available. The company has 1500 units of foam backing available for use.
a. State the problem as a linear program on a sheet of paper
b. Solve the linear program in Excel.
c. What is the value of the objective function?
d. What are the binding constraints?
e. How much would the profit increase if another 100 units of synthetic fiber were made available?