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.

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.

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

Just do:
$$
R(55)-C(55)
$$