Production. 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 $P ( t ) :$ $P ( t ) = 90 t + 42 t ^ { 2 } - 2 t ^ { 3 }$ . Find the number of hours before the rate of production is maximized. That is, find the point of diminishing returns.
A) $t = 0$
B) $t = 7$
C) $t = 5$
D) $t = 8$
E) $t = 15$

Question

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The Answer of Production. 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 $P ( t ) :$ $P ( t ) = 90 t + 42 t ^ { 2 } - 2 t ^ { 3 }$ . Find the number of hours before the rate of production is maximized. That is, find the point of diminishing returns.
A) $t = 0$
B) $t = 7$
C) $t = 5$
D) $t = 8$
E) $t = 15$

Production P(t):P ( t ) :P(t): P(t)=90t+42t2−2t3P ( t ) = 90 t + 42 t ^ { 2 } - 2 t ^ { 3 }P(t)=90t+42t2−2t3

Production $P ( t ) :$ $P ( t ) = 90 t + 42 t ^ { 2 } - 2 t ^ { 3 }$