Asked by cb

3q2+5q+300

Find the marginal and average cost functions.

Show that AC is at its minimum when
q = 10 and that MC = AC at this output

Answers

Answered by economyst
Marginal cost is the first derivitive of the total cost function. So,,
MC = 6q + 5

AC = 3q + 5 + 300/q. To find the minimum AC, take the first dirivitive and set equal to zero.
AC' = 3 - 300/q^2 = 0. Solve for q. Thus, q=10 at the minimum of the AC curve. So, at q=10 AC = 30+5+30 = 65
and MC = 60+5 = 65

QED
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