Question

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

Answer 1

The answers to the question are:

• The machine that is the constraint is the machine c.
• The product m = 80 units and n = 80 units
• Net profit = $3600

1. How to solve for the constraint of the machine

We have to solve for the workload of the machines

For A. 20*100 = 2000

For B, 5 * 100 + 10 *80

= 500 + 800 = 1300

For Machine C = 15 * 100 + 15 * 80

= 1500 + 1200

= 2700

The time at the workstation in c is more than the constant time of 2400, hence the constraint that we have is machine c.

b. 2400- 1200 = 1200

The product mix would be 1200/15

= 80

Hence the product mix m = 80 units and that of n = 80 units

c. The total net profit

80*$90 = 7200 , 80 * 105 = 8400

7200 + 8400

= 15600

The net profit = 15600 - 12000

= $3600

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