A manufacturer’s cost (in dollars) is

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

Problem

C(q)=100+0.5q^{2}

, where

q

is the number of units demanded. Demand depends on price

p

(in dollars) through

q(p)=200-4p

. At the moment when the price is

p=25

and decreasing at

\dfrac{dp}{dt}=-0.10\text{ dollars/week}

, determine the rate of change of cost with respect to time,

\dfrac{dC}{dt}

. Express your answer with appropriate units.