Question

Revenue is given by R(q)=550q and cost is given by C(q)=10000+5q^2
A)At what quantity is profit maximized?
B)What is the total profit at this production level? Give your answer without commas.

Answer 1

We wish to maximize:
\[
R-C=P
\]Where \(P\) is profit and all functions are defined on \(q\). So, we have:
\[
\max_{q\in \mathbb{R}}\left(550q-10000-5q^2\right)
\]So, we take the derivative to find the vertex:
\[
\frac{d}{dq}\left(550q-10000-5q^2\right)=550-10q=0\implies\\
q=55
\]Hence we are done.
For (B), simply evaluate \(P(q)\) as defined above.

Answer 2

thanx man really appreciate it can u help me wit B) im on a timed test

Answer 3

Just do:
\[
R(55)-C(55)
\]