The weekly production cost in dollars for a product is modelled by

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The weekly production cost

C

in dollars for a product is modelled by

C(q)=40q+0.05q^2

, where

q

is the weekly demand in units. Demand depends on the selling price

p

in dollars through

q(p)=1500-25p

. At the moment when the price is

20

dollars and is falling at a rate of

0.80

dollars per week, what is

\frac{dC}{dt}

? (a)

-2.8\times10^3\ \text{dollars per week}

(b)

2.8\times10^3\ \text{dollars per week}

(c)

3.5\times10^3\ \text{dollars per week}

(d)

1.8\times10^3\ \text{dollars per week}