Tucker Inc. produces high-quality suits and sport coats for men. Each suit requires 1.2 hours of cutting time and 0.7 hours of sewing time, uses 6 yards of material, and provides a profit contribution of $190. Each sport coat requires 0.8 hours of cutting time and 0.6 hours of sewing time, uses 4 yards of material, and provides a profit contribution of $150. For the coming week, 200 hours of cutting time, 180 hours of sewing time, and 1200 yards of fabric are available. Additional cutting and sewing time can be obtained by scheduling overtime for these operations. Each hour of overtime for the cutting operation increases the hourly cost by $15, and each hour of overtime for the sewing operation increases the hourly cost by $10. A maximum of 100 hours of overtime can be scheduled. Marketing requirements specify a minimum production of 100 suits and 75 sport coats. Let
S = number of suits produced
SC = number of sport coats produced
D1 = hours of overtime for the cutting operation
D2 = hours of overtime for the sewing operation
The computer solution developed using The Management Scientist is shown in Figure.
THE MANAGEMENT SCIENTIST SOLUTION FOR THE TUCKER INC. PROBLEM

a. What is the optimal solution, and what is the total profit? What is the plan for the use of overtime?
b. A price increase for suits is being considered that would result in a profit contribution of $210 per suit. If this price increase is undertaken, how will the optimal solution change?
c. Discuss the need for additional material during the coming week. If a rush order for material can be placed at the usual price plus an extra $8 per yard for handling, would you recommend the company consider placing a rush order for material? What is the maximum price Tucker would be willing to pay for an additional yard of material? How many additional yards of material should Tucker consider ordering?
d. Suppose the minimum production requirement for suits is lowered to 75. Would this change help or hurt profit?Explain.

Objective Function Value- 40900 000 Variable Value Reduced Costs SC D1 D2 100.000 150.000 40.000 0.000 0:000 0.000 0.000 10.000 Constraint Slack/Surplus Dual Prices 0.000 20.000 0.000 60.000 0.000 75.000 15.000 0.000 34.500 0.000 35.000 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Linit Current Value Upper Limit SC D1 D2 No Lower Linit 126.667 -187.500 No Lower Linit 190.000 150.000 -15.000 -10.000 225.000 No Upper Limit 0.000 0.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 140.000 160.000 1000.000 40.000 0.000 No Lower Linit 200.000 180.000 1200.000 100.000 100.000 75.000 240.000 No Upper Limit 1333.333 No Upper Limit 150.000 150.000