The total cost in dollars of producing x lawn mowers is given by C(x) = 4000 + 9

Question

The total cost in dollars of producing x lawn mowers is given by C(x) = 4000 + 90x = x^2/3. Find the marginal average cost at x = 20. C'(20) and interpret the result. Select one: A. -$13.33 a unit increase in production will decrease the average per unit by approximately $13.33 at a production level of 20 units. B. -$20.33 a unit increase in production will decrease the average cost per unit by approximately $20.33 at a production level of 20 units. C. -$1.33, a unit increase in production will decrease the average cost per unit by approximately $1.33 at a production level of 20 units. D. -$10.33, a unit increase in production will decrease the average cost per unit by approximately $10.33 at a production level of 20 units.

Explanation / Answer

Average cost = C(x) = C(x)/x = (4000 + 90x - x^2/3)/x

C(x) = 4000/x + 90 - x/3

Marginal average cost = C'(x) = d(C(x))/dx

C'(x) = = -4000/x^2 + 0 - 1/3

C'(x) = -(4000/x^2 + 1/3)

at x = 20

C'(x) = = -(4000/20^2 + 1/3) = -$10.33

Since average cost is negative, it's decreasing,

Correct option is D.

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