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Suppose that the total number of units produced by a worker in t hours of an 8-hour shift can be modeled by the production function

Suppose that the total number of units produced by a worker in t hours of an 8-hour shift can be modeled by the production function

P(t).

P(t) = 15t + 6t2 t3

(a) Find the number of hours before production is maximized. (b) Find the number of hours before the rate of production is maximized. That is, find the point of diminishing returns.

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