A sport goods company wants to determine the number of All-Pro and College footballs to produce in order to maximize profit. Constraints affecting the production quantities are the production capacities in three departments: cutting and dyeing; sewing; and inspection and packaging. There are 550 hours of cutting and dyeing time, 400 hours of sewing time, and 150 hours of inspection and packaging time available. Each All-Pro football requires 15 minutes of cutting and dyeing time, 10 minutes of sewing time, and 12 minutes of inspection and packaging time. Each College football requires 12 minutes of cutting and dyeing time, 10 minutes of sewing time, and 10 minutes of inspection and packaging time.The company wants to produce at least 500 All-pro footballs and at least 350 College footballs. Each All-Pro football provides a profit of $16.50 and each College football provides a profit of $11.50.Formulate a linear programming model for the above situation by determining (a) The decision variables(b) Determine the objective function. What does it represent?(c) Determine all the constraints. Briefly describe what each constraint represents.