Golf Shafts, Inc. (GSI)) produces graphite shafts for several manufacturers of golf clubs. Two GSI manufacturing facilities, one locate in San Diego and the other in Tampa , have the capabilities to produce shafts in varying degrees of stiffness, ranging from regular models used primarily by regular golfers and extra stiff models used primarily by low handicap and professional golfers. GSI just received a contract for the production of 200,000 regular shafts and 75,000 stiff shaft. Because both plants are currently producing shafts for previous orders, neither plant has sufficient capacities by itself to produce the new order. The San Diego plant can produce a total of 120,000 shafts and the Tampa plant can produce up to a total of 180,000 shafts. Because of equipment differences at each of the plants and different labor costs, the per-unit production costs vary as shown here:
San Diego Costs Tamps Costs
Regular shafts $5.25 $4.95
Stiff Shafts $5.45 $5.70
a) Formulate a linear programming model to determine how GSI should schedule production for the new order in order to minimize the total production cost.
b) Solve the model for part A
c) Suppose that some of the previous orders at the Tampa plant could be rescheduled in order to free up additional capacity for the new order. Would this option be worthwhile?
d) Suppose that the cost to produce stiff shafts in Tamps had been incorrectly computed, and the correct cost is $5.30 per shaft What effect if any would the correct cost have on the optimal solution developed in part (b)? What effect would it have on total cost?