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Ace Custom Flooring makes two different grades of commercial carpets for local businesses. In the coming production cycle, Ace needs to decide how many rolls of each grade should be produced in order to maximize the profit. Each roll of Grade X1 carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade X2 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 X1 carpet is $210 and the profit per roll of Grade X2 carpet is $160. In the coming cycle, Ace has 3000 units of synthetic fiber available. Workers have been scheduled to provide at least 1800 hours of production time (with possible overtime). The company has 1500 units of foam backing available for use. Lastly, the manager has decided that no more than 50 rolls of Grade X2 carpet be produced. (a) Write the LP formulation to determine the number of rolls of both grades of carpet in order to optimize profit. Use your scrap page. (b) Write the above LP formulation in Standard Form. (c) Using your grid page, graph the LP formulation for the above problem. Be sure to label the axes, constraints, and feasible region. (d) Determine the coordinates of each extreme point and its corresponding profit. Use 1 or 2 decimal places only if needed. For the above LP problem, answer the following questions here. You must show all of your work on the scrap pages to receive full credit. (a) What is the optimal solution? Write as an ordered pair. Use 1 decimal only if needed. (b) What is the value of the objective function at the optimal solution? Use 2 decimal places. $ (c) Which constraints are binding? Use constraint numbers. (d) What is the Slack/Surplus for the non-binding constraint(s). Interpret it; ie, 50 hours of finishing time, slack