Question

Total profit is defined as total revenue, R(x), minus total cost, C(x), and is given by the function P(x) = R(x) - C(x). Given R(x) = 58x -0.4x^2and C(x) = 2x + 14, find each
of the following.
a) P(x)
b) R(80), C(80), and P(80)
P(x)=
(Type in descending powers of x.)

Answer 1

$\bf \begin{cases} R(x)=58x-0.4x^2\\ C(x)=2x+14 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ P(x)\implies \stackrel{revenue}{R(x)}-\stackrel{costs}{C(x)}\implies (58x-0.4x^2)-(2x+14) \\\\\\ (58x-0.4x^2)-2x-14\implies 58x-0.4x^2-2x-14 \\\\\\ 56x-0.4x^2-14\implies \boxed{-0.4x^2+56x-14} \\\\[-0.35em] ~\dotfill$

$\bf R(80)\implies 58(80)-0.4(80)^2\implies R(80)=4640-2560\implies \boxed{R(80)=2080} \\\\[-0.35em] ~\dotfill\\\\ C(80)=2(80)+14\implies C(80)=160+14\implies \boxed{C(80)=174} \\\\[-0.35em] ~\dotfill\\\\ P(80)=-0.4(80)^2+56(80)-14 \\\\\\ P(80)=-2560+4480-14\implies \boxed{P(80)=1906}$