Reference no: EM13337878
Formulate a goal programming model that describes the followingmanufacturing situation. Identify your decision variablescompletely and label constraints with a brief word explanation. Watch your units! DO NOT RUN THIS PROBLEM!!
The Grand American Bicycle Co. (GAB) must determine a productionschedule for the next four weeks. Three products are in question:BMX, mountain (Berg), and racing (RR) bicycles. A toy store chainwants 500 BMX bikes from GAB while GAB’s largest customer hasrequested 600 Berg bikes. Because RR bikes bring in $100 profiteach, they may be more attractive to make than the BMX (with aprofit of $20) and the Berg bikes (with a profit of $55). RR bikestake a good amount of time in the welding room, as they must bebuilt precisely. A BMX frame takes 4 minutes, a Berg frame 10minutes, and a RR frame 45 minutes. The welding room is normallyoperated 8 hours a day, 5 days per week. Each bicycle needs a pairof pedals; there are expected to be 2500 pedals on hand at thestart of the production period. The BMX frame requires 98 inches oftubing, while the frame of a Berg bike requires 140 inches oftubing, and a RR bike requires 130 inches of tubing; there are4,000 yards of tubing in stock. Management has set priorities inthe following order:
I. Avoid overtime in the welding room.
II. Satisfy known orders, weight differentially according to unitprofits.
III. Avoid buying more supplies.
IV. Use up all available welding time.
V. Maximize profit.
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Examples of alternate hypothesis and rejection region
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Formulate a goal programming model
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