Lulu Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Lulu Manufacturing 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, Lulu Manufacturing has 3000 units of synthetic fiber available for use. Each of the 10 workers have been scheduled to provide at least 180 hours of production time. The company has 1500 units of foam backing available for use. Based of the previous sales data, Lulu Manufacturing needs to produce at least 20 Grade X carpet and 30 Grade Y carpet to fulfill customers demand.

(a) Develop a linear programming model for this problem.

(b) Use LP graphical method to determine the most profitable number of table and chair, and its optimal profit.

(c) If the company has only 750 units of foam backing available to use, what would happen? Explain.

(d) If the problem is to minimize instead of maximize, use the isocost method to find the optimal solution.