Question

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.

Answer 1

a. The optimal solution calls for the production of 100 suits and 150 sport coats. Forty hours of cutting overtime should be scheduled, and no hours of sewing overtime should be scheduled. The total profit is $40,900.

 

b. The objective coefficient range for suits shows and upper limit of $225. Thus, the optimal solution will not change. But, the value of the optimal solution will increase by ($210-$190)100 = $2000. Thus, the total profit becomes $42,990.

 

c. The slack for the material coefficient is 0. Because this is a binding constraint, Tucker should consider ordering additional material. The dual price of $34.50 is the maximum extra cost per yard that should be paid. Because the additional handling cost is only $8 per yard, Tucker should order additional material. Note that the dual price of $34.50 is valid up to 1333.33 -1200 = 133.33 additional yards.

 

 

The dual price of -$35 for the minimum suit requirement constraint tells us that lowering the minimum requirement by 25 suits will improve profit by $35(25) = $875.