A company has a linear total cost function and has determined that over the next three months it can produce 12,000 units at a total cost of $224,000. This same manufacturer can produce 18,000 units at a total cost of $296,000. The selling price per unit is $13.25. i. Determine the revenue, cost and profit functions using q for number of units. ii. What is the fixed cost ? iii. What is the marginal cost ? iv. Find the break-even quantity. v. What is the break-even dollar volume of sale ? vi. What will profit be if the company shuts down operation? vii. If, because of a strike, the company will be able to produce only 10,000 units, should it shut down for the next three months ? why or why not ?
i. The revenue, cost and profit functions using q for number of units are:
TR = 13.25q,
"\\frac{TC - 224,000} {296,000 - 224,000} = \\frac{q - 12,000} {18,000 - 12,000},"
"\\frac{TC - 224,000} {12} = \\frac{q - 12,000} {1},"
"TC - 224,000 = 12q - 144,000,"
TC = 12q + 80,000.
TP = TR - TC = 1.25q - 80,000.
ii. The fixed cost is:
FC = 80,000.
iii. The marginal cost is:
MC = TC'(q) = 12.
iv. The break-even quantity is:
"BEQ = 80,000\/(13.25 - 12) = 64,000."
v. The break-even dollar volume of sale is:
TR = 13.25×64,000 = 848,000.
vi. The company shuts down operation at P < AVC or P < 12.
vii. If, because of a strike, the company will be able to produce only 10,000 units, then:
TP = 1.25×10,000 - 80,000 = -67,500.
But it should not shut down for the next three months, because it can cover its variable costs.
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