The number of units Q of a particular commodity that will be produced when L worker-hours of labor are employed is modeled by

Suppose that the labor level varies with time in such a way that t months from now L(t) worker-hours will be employed, where

for 0 ≤ t ≤ 12.

a. How many worker-hours will be employed in producing the commodity 5 months from now? How many units will be produced at this time?

b. At what rate will production be changing with respect to time 5 months from now? Will production be increasing or decreasing at this time?

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Q(L) = 300L¹/3