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A manufacturer of clothing makes pants, shirts, and jackets. The profit on a pair of pants is $12.00, on a shirt is $8.00, and on a jacket is $18.00. All three garmentsrequire the work of sewing operators and cutters. There are 60 hours of sewing operator time and 48 hours of cutter time available. It takes 10 minutes to sew one pair of pants, 6 minutes to sew a shirt, and 14 minutes to sew one jacket. Cutters take 6 minutes per pair of pants, 8 minutes per shirt, and 10 minutes per jacket. Furthermore, each item should undergo a final quality control inspection. An inspection takes 1 minute per a pair of pants, 2 minutes per shirt, and 3 minutes per jacket. There are 12 hours of quality control operator time available.

a) Formulate a linear program to find the optimal numbers of pants, shirts, and jackets that maximize profit. Clearly define your decisions variables, objective function and constraints.

b) Implement your formulation in Excel and use Solver to find the optimal solution. Provide answers for the optimal amounts and objective function value. Provide an organized screen shot of your solution

c) Using the sensitivity analysis report, what will be the impact of increasing the number of producing one additional shirt? Find the answer without solving the problem again

d) Using sensitivity analysis report, suppose that the new profit per jacket is $30. Find the new optimal solution and profit

e) Management is considering adding an extra 50 minutes of labor time. Would you recommend adding this time to sewing, cutting, or quality control? (Provide a detailed justification of your recommendation).