Please fully explain the three parts

XYZ Ltd produces two popular grades of commercial carpeting among its many other products. In the coming production period, XYZ needs to decide how many rolls of each grade should be produced in order to maximize total profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 10 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, XYZ 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. XYZ wants to develop and solve a linear programming model for this problem. Note: Provide your answers in the space indicated below. a. (10 p.) Define the decision variables. b. (10 p.) Define the objective function. c. (10 p.) Define the constraints