Kate's Fashion Designs produces four clothing products in one of its factories. Kate produces slacks, dresses, skirts, and blouses. Production of these items is limited by the capacity of four areas: cutting, sewing, inspecting and packing. Hours per week in the departments respectively: 800 hours per week, 700, 600, and 660.

The following chart shows the required hours per item in each department.

a) Which departments have capacities that limit output?

b) The plant manager is considering scheduling overtime. Is there any department or departments that should be excluded from consideration?

c) What is the value of overtime scheduled in the cutting department? How much overtime could be effectively used?

d) Overtime costs the company a premium of $3 per hour over regular costs. If one department is scheduled for overtime, which one should be scheduled, and how much overtime can be effectively used?

What would the revised optimal value of the objective function be, including an allowance for the premium?

e) If the unit profit on skirts dropped by 50 percent, how would that affect the optimal values of the decision variables and the optimal value of the objective function?

f) What would the profit per unit on slacks have to be before the company would want to begin producing them?