Broadway Sports Products wants to determine the number of All-Pro (A) and College (C) footballs to produce in order to maximize profit over the next four- week planning horizon. Constraints affecting the production quantities are the production capacities in three departments: cutting and dyeing; sewing; and inspection and packaging. For the four-week planning period, 340 hours of cutting and dyeing time, 420 hours of sewing time, and 200 hours of inspection and packaging time are available. All-Pro footballs provide a profit of $5 per un and use 12 hours for cutting and dyeing, 9 hours for sewing, and 6 hours for inspection and packing. College footballs provide a profit of $4 per unit and use 8 hours for cutting and dyeing, 13 hours for sewing, and 6 hours for inspection and packing. Write the linear programming model (variables, objective function, and constraints) with production times expressed in hours