16. 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 material 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 sensitivity report is shown in Figure 8.20. 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 that 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.

FIGURE 8.20 SENSITIVITY REPORT FOR THE TUCKER INC. PROBLEM Variable Cells Model Variable S SC D1 D2 Name Suits Produced Coats Produced Overtime for Cutting Overtime for Sewing Final Value 100.000 150.000 40.000 0.000 Reduced Cost 0.000 0.000 0.000 - 10.000 Objective Coefficient 190.000 150.000 -15.000 -10.000 Allowable Increase 35.000 1E+30 15.000 10.000 Allowable Decrease 1E+30 23.333 172.500 1E+30 Constraints Constraint Number 1 2 3 4 5 6 Name Cutting time Sewing time Material Overtime Suit minimum Sport coat minimum Final Value 200.000 160.000 1200.000 40.000 100.000 150.000 Shadow Price 15.000 0.000 34.500 0.000 -35.000 0.000 Constraint R.H. Side 200.000 180.000 1200.000 100.000 100.000 75.000 Allowable Increase 40.000 1E+30 133.333 1E+30 50.000 75.000 Allowable Decrease 60.000 20.000 200.000 60.000 100.000 1E+30 lo Cengage Leaming 2013