A carpet 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.

• Formulate and solve a linear programming model using graphical analysis for this problem by showing the feasible region, mark all corner points and determine the optimal solution.
• Now, suppose that the manager wants to increase the profit per roll of Grade X carpet by 25 percent and decrease the profit per roll of Grade Y carpet by 10 percent. What this action do to the solution?
• Refer to your original solution, suppose the manager did not change any profits per roll for both carpets, but he changed the production time for Grade X from 25 hours to 20 and for Grade Y from 28 to 25 hours of production time. What does this do to your original solution?