Pls formula a linear programming model.

2.3 A film packaging plant can manufacture four different thicknesses (1, 3, 5, and 0.5 mm) in any combination. Each thickness requires time on each of three machines in minutes per square yard of film, as shown in the table below. Each machine is available 60hours per week. The table also gives revenue and cost per square yard for each thickness. Variable labor costs are $25)per hour for machines 1 and 2, and $35) per hour for machine 3. Formulate and solve a profit-maximizing LP model for this problem, given the maximum demands for each thickness. 96 Thickness Imm 3mm 5mm 0.5mm Time (min) 1 2 5 5 8 9 4 7 5 4 5 4 6 10 6 Max Demand Revenue Cost 400 $110 $30 250 S90 $10 200 S60 $10 450 $100 $20 a) Formulate a linear programming model for this problem. b) Solve the linear program using the IBM ILOG CPLEX Optimization Studio