### Optimal combinations of labor and capital

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What are the following answers and the formula used?

The production engineers at Impact Industries have derived the optimal combinations of labor and capital (the only two inputs used by Impact) for three levels of output: 120, 180, and 240 units of output:

Q           L*          K*

120        4            20

180        6            30

240        8            50

Q is the output level, L* is the optimal amount of labor to use, and K* is the optimal amount of capital to use. The price of labor is \$100 per unit and the price of capital is \$20 per unit.

a) If the manager of Impact Industries decides to produce 120 units, what will the long-run total cost and long-run average cost of producing 120 units?

b) If the manager of Impact Industries decides to produce 180 units, what will the long-run total cost and long-run average cost of producing 180 units?

c) If the manager of Impact Industries decides to produce 240 units, what will the long-run total cost and long-run average cost of producing 240 units?

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