Question

The marketing research department for a company that manufactures and sells laptop computers

established the following price-demand and cost functions, respectively:

p (x) = 1,000 - 25x

C(x) = 2,150 + 250x

where p() is the wholesale price in United States dollars at which y thousand laptops can be sold and

C(x) is in thousands of dollars. The domain of both functions is, 1 < x < 10.

formulate a revenue and a profit function

Answer 1

The revenue function is given as : $R(x)=P(x)×x$

$R(x)=(1000-25x)x$

$R(x)=1000x-25x^2$

The profit function, $\pi(x)$, is given as: $\pi(x)=R(x)-C(x)$

$\pi(x)=1000x-25x^2-(2150+250x)$

$\pi(x)=1000x-25x^2-2150-250x$

$\pi(x)=750x-25x^2-2150$