Problem $22$S$-17($Algo$)$

The M$$N plant manufactures two different products: M and N$.$ Selling prices and weekly market demands are shown in the following diagram. Each product uses raw materials with costs as shown. The plant has three different machines: A$,$ B$,$ and C$.$ Each performs different tasks and can work on only one unit of material at a time.

Process times for each task are shown in the diagram. Each machine is available $2,700$ minutes per week. There are no "Murphys" $($major opportunities for the system to foul up$).$ Setup and transfer times are zero. Demand is constant.

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Operating expenses $($including labor$)$ total a constant $$10,000$ per week. Raw materials are not included in weekly operating expenses.

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a$.$ Which machine is the constraint in this plant?

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multiple choice

Machine A

Machine B

Machine C

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b$.$ Which product mix provides the highest gross profit? $($Hint: consider raw material cost but not operating expense$)$

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c$.$ What is the maximum weekly net profit this plant can earn using the product mix from Part b$?($Hint: consider operating expense and raw material cost$)$

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