Question

Given the revenue function R(x)= 100x −2x^2 (space) 1 ≤ x ≤ 30 and the cost function C(x)= 500 + 9x for a company, find the profit if the company produces 25 units. Do not include a dollar sign in your answer. For example, if your answer is $315.12, enter 315.12.

Answer 1

well, once you take in all the Revenue from sales, and subtract all the costs that went in for the product, what's leftover is the Profit.

so then, profit P(x), is simply the revenue minus costs, namely P(x) = R(x) - C(x)

`R(x)=100x-2x^2\hspace{5em}C(x)=500+9x \\\\\\ P(x)=(100x-2x^2)~~ - ~~(500+9x)\implies P(x)=91x-2x^2-500 \\\\\\ \stackrel{\textit{at a production of 25 units, x =25}}{P(25) = 91(25)-2(25)^2-500}\implies P(25)=\stackrel{2275-1250-500}{525}`