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 60 hours 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. We wish to maximize profit given the maximum demands for each thickness that the market can handle. Time on machines 2 3 8 9 7 5 5 4 10 6 Thickness 1 1mm 5 2mm 4 5mm 4 0.5mm 6 Max demand 400 250 200 450 Revenue Cost $110 $30 $90 $10 $60 $10 $100 $20 (a) What are your decision variables? In terms of those decision variables, what is the objective function? (b) Formulate this problem as a linear program. (c) Solve the linear program using LINGO and interpret your answer.