A goatherd has the cost function c(y) = 4y2, where y is the number of tubs of goat cheese she makes per month. She faces a competitive market for goat cheese,with a price of $40 a tub. How many tubs should she produce per month?
A) The square root of 40
B) 16
C) 5
D) The square root of 10
E) 2.50

Question

Quizplus · Accepted Answer

To find the optimal level of production, we need to equate the marginal cost with the price.
The marginal cost is the derivative of the cost function with respect to y, which is:
c'(y) = 8y

Setting this equal to the price of $40 per tub, we get:
8y = 40
y = 5

Therefore, the goatherd should produce 5 tubs of goat cheese per month to maximize her profit.

A Goatherd Has the Cost Function C(y) = 4y2, Where