only set-up the linear programming formulations for parts a) and d - you do not need to solve for the answer to either part. 23. Supertronics, Inc., would like to know how the firm's profitability is altered by product mix. Currently, product mix is determined by giving priority to the product with the highest per-unit contribution margin (defined as the difference between price and material cost). Details on the Supertronics product line, including processing time at each workstation, follow: PRODUCT Alpha Beta Delta Gamma Price $350.00 $320.00 $400.00 $500.00 Material Cost $50.00 $40.00 $125.00 $150.00 Weekly Demand in Units 100 60 50 80 Processing Time at Machine 1 in Minutes 20 40 10 Processing Time at Machine 2 in Minutes 25 20 50 Processing Time at Machine 3 in Minutes O 20 60 30 a. Assume that Supertronics has 5,500 minutes of capacity available at each workstation each week. Develop a linear program to define the production mix that maximizes contribution margin. b. Solve your formulation using a computer package such as POM for Windows. c. Given your solution for part (b), which machine is the bottleneck? d. How would your formulation and solution in part (b) change if 50 units of each product were already committed to customers and thereby had to be produced