Golf Shafts, Inc. (GSI), produces graphite shafts for several manufacturers of golf clubs. Two GSI manufacturing facilities, one located in San Diego and the other in Tampa, have the capability to produce shafts in varying degrees of stiffness, ranging from regular mod- els used primarily by average golfers to extra stiff models used primarily by low-handicap and professional golfers. GSI just received a contract for the production of 200,000 regu- lar shafts and 75,000 stiff shafts. Because both plants are currently producing shafts for previous orders, neither plant has sufficient capacity by itself to fill the new order. The San Diego plant can produce up to 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 differing labor costs, the per-unit production costs vary as shown here:
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Regular shaft
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San Diego Cost
$5.25
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Tampa Cost
$4.95
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Stiff shaft
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$5.45
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$5.70
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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 that you developed in 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 worth- while? Explain.
d. Suppose that the cost to produce a stiff shaft in Tampa had been incorrectly computed, and that 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 production cost?