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Production Function

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Consider the following short-run production function (where L= variable input, Q= output): Q = 6L to the second power - .4L to the third.

a. Find the value of L that maximizes Q.

b. Fin the value of L at which the marginal product function takes on its maximum value.

c. Find the value of L at which the average product function take on its maximum value.

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Q = 6L^2 - 0.4L^3

(a) To maximize Q, we set dQ/dL to zero and solve for L.
dQ/dL = 12L - 1.3L^2 = 0
or L(12 - 1.3L) = 0
which gives L = 0, ...

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