Production cost in dollars is

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Production cost in dollars is C(d)=0.05d2+40dC(d)=0.05d^{2}+40d, where dd units are demanded when the price is pp dollars according to d(p)=1000−20pd(p)=1000-20p. The price changes with time as p(t)=25+3sin⁡(0.2t)p(t)=25+3\sin(0.2t), where tt is measured in days. Determine dCdt\dfrac{dC}{dt} at t=0t=0 and state the units of your answer.

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