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.

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Process times for each task are shown in the diagram. Each machine is available 3,500 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 B
Machine C
b. Which product mix provides the highest gross profit? (Hint: consider raw material cost but not operating expense) - in units

Product M:
Product N:
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)

Weekly Net Profit

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topeadeniran2 topeadeniran2 · Answer 1 · 2022-08-17T18:40:41+02:00

The machine that is the constraint in this plant is Machine C.

From the information, the total available time is given as 2400 minutes per week. The aggregate workload for each machine will be:

A = 20 × 100 = 2000

B = (5 × 100) + (8 × 100) = 1300

C = (15 × 100) + (15 × 80) = 2700

For C, the available time per week is 2400. Therefore, this is the constraint.

The product mix that provides the highest gross profit will be:

M = 1200/15

M = 80 units.

Also, for product N, the units will be 80 units.

The maximum weekly net profit this plant can earn using the product mix will be:

= (80 × 90) + (80 × 105) - 12000

= 7200 + 8400 - 12000

= $3600

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