Question

Humax Manufacturing produces two popular grades of commercial synthetic grass among its many other products. In the coming production period, the manager needs to decide how many rolls of each grade should be produced to maximize profit. Each roll of Grade X grass carpet uses 50 units of synthetic grass fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y grass carpet uses 40 units of synthetic grass fiber, requires 28 hours of production time, and needs 15 units of foam backing.

The profit per roll of Grade X grass carpet is $200 and the profit per roll of Grade Y grass carpet is $160. In the coming production period, Xylo has 3000 units of synthetic grass 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.

Develop the linear programming model and solve this problem completely using the graphical method. What is the optimal solution?

Solve graphically this problem graphically. Please submit your hand-drawn graph.

Answer 1