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 $3,100$ minutes per week. There are no

"Murphys" $($major opportunities for the system to foul up$).$ Setup and transfer times are zero. Demand is constant.

Operating expenses $($including labor$)$ total a constant $$12,000$ per week. Raw materials are not included in weekly

operating expenses.

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

Machine A

Machine C

Machine B

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

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$)$