The Eaststate Manufacturing Company produces four different airplane parts from fabricated sheet metal for several major aircraft companies. The manufacturing process consists of four operations€”stamping, assembly, finishing, and packaging. The processing times per unit for each operation and total available hours per year to produce these parts are as follows:

The sheet metal required for each part, the estimated annual demand, and the profit per part are as follows:

The company has 15,000 square feet of fabricated metal delivered each month. The company has the following prioritized production goals:
(1) Avoid overtime, which would erode profit levels.
(2) Meet parts demand.
(3) Achieve an annual profit of $700,000.
(4) Avoid ordering more material because a surcharge is required by the supplier for changing the standard monthly order.
a. Formulate a goal programming model to determine the amount of each part to produce to achieve the company€™s objectives.
b. Solve this model by using the computer.
c. How would the solution be affected if the first two priorities werereversed?

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Part (hr./unit) Operation 4 Total Hours/Year Stamping Assembly Finishing 0.07 Packaging 0.09 0.2 0.07 0.15 0.06 017 0.100.14 0.14 0.12 700 700 800 600 0.20 0.20 0.18 0.08 Sheet Estimated Annual Demand Part Metal (ft.2) Profits 2.6 1.4 2.5 3.2 2,600 1,800 4,100 1,200 $ 90 100 80 120 4