Cost Function Question

Question

For the cost function C(x) = 529+50 x + x^2 find:
a) The cost at the production level 160
b) The average cost at the production level 160
c) The marginal cost at the production level 160
d) The production level that will minimize the average cost

Answer 1

(a) Compute 529 + 50(160) + 160² equal to $34129.00.

(b) Take average cost as 34129 ÷ 160 or 213.30625 equivalent to $213.31.

(c) Differentiate 529 + 50x + x² to obtain 50 + 2x; then marginal cost is 50 + 2(160)

or $370.00.

(d) Write (529 + 50x + x²) ÷ x or 529x^-1 + 50 + x which differentiates to 1 − 529/x².

Equate this last to zero which forces x² to 529 and x to √529 or a production level

of 23 units.