Question

The marketing research department for a company that manufactures and sells computers established the following price-demand and cost functions. p(x)=2262-63x   where p(x) is the wholesale price per computer in dollars at which x thousands of computers can be soldC(x)=4151+599xwhere C(x) is the cost in thousands of dollars. Domain of both functions is 0≤x≤35. 1. Find the Maximum Revenue (in thousands of dollars) R_Max(x)=
(Round to 3 d.p.)

Answer 1

$R(x)=x(p(x))=x(2262-63x)=2262x-63x^2$

$\frac{d}{dx}(2262x-63x^2)=0$

$2262-63x=0$

$x=\frac{-2262}{-126}$

$x=17.95238095238\approx17.952$

$R_{max}x\approx17.952 \space thousands\space of\space dollars$