1. 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 prot. Each roll of Grade K carpet uses 50 units of synthetic ber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic ber, requires 28 hours of production me, and needs 15 units of foam backing. The prot per roll of Grade K carpet is $200 and the prot per roll of Grade '1' carpet is $160. In the coming production period, Muir has 3000 units of synthec ber 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 the problem as a linear program