Question

The total cost (in dollars) for a company to manufacture and sell a items per week is C(x) = 40x + 500. If the revenue brought in by selling all a items is R(x) = 60x -0.05x2, find the weekly profit. How much profit will be made by producing and selling 80 items each week? Hint: P(x) = R(x) - C(x).P(x) =P(80) = $

Answer 1

$\begin{gathered} P(x)=-0.05x^{2}+20x-500 \\ P(80)=780 \end{gathered}$Explanation

give

$\begin{gathered} Cost\text{ function C\lparen x\rparen=40x+500} \\ Revenue\text{ function R\lparen x\rparen=60x-0.05x}^2 \end{gathered}$

Step 1

find the profit function

$\begin{gathered} P(x)=R(x)-C(x) \\ replace \\ P(x)=60x-0.05x^2-(40x+500) \\ break\text{ the parenthesis} \\ P(x)=60x-0.05x^2-40x-500 \\ add\text{ like terms} \\ P(x)=-0.05x^2+20x-500 \end{gathered}$

Step 2

now, evaluate for x=80

$\begin{gathered} P(x)=20x-0.05x^2-500 \\ P(80)=-0.05(80)^2+20(80)-500 \\ P(80)=-320+1600-500 \\ P(80)=780 \end{gathered}$

so, the answer is

$\begin{gathered} P(x)=-0.05x^{2}+20x-500 \\ P(80)=780 \end{gathered}$

I hope this helps you