Question

For the given cost function

C(z) = 22500 + 600x + x² find:
a) The production level that will minimize the average cost
b) The minimal average cost

Answer 1

• 150 units
• 900 per unit

Explanation:

For the cost function C(x) = 22500 + 600x + x² you want to find a) the production level that will minimize the average cost, and b) the minimal average cost.

a) Average cost

The average cost is the total cost divided by the number of units produced.

Cavg = C(x)/x = 22500/x + 600 + x

This will be a minimum where its derivative is zero:

Cavg' = -22500/x² +1 = 0

x² = 22500

x = 150

The production level that minimizes average cost is x = 150 units.

b) Minimum average cost

Cavg(150) = 22500/150 +600 +150 = 900

The minimum average cost is 900 per unit.

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