QUESTION Mal Manufacturing Inc. produces two popular grades (grade X and Y) of commercial carpeting among its many other products. In the coming production period, Mal Manufacturing Inc. 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, Mal Manufacturing Inc. 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. Note that the company need to produce both grade X and Y carpets, and the number of roll need to be in whole number. (a) Develop a mathematical model for the problem (b) Using Linear Programming Graphical Method, find the feasible region for the problem (c) Use Corner Point Method to find the optimal solution for the problem
