Economics help - Maximum Profit?

Question

The only Chinese restaurant in town has a total cost function of TC=25+Q+5Q^2. The demand function in town for Chinese food is Q=25-P. What is the restaurants maximum profit?

Answer 1

Simplified short-run profit-maximization rule is MR=MC, thus:
MR=∂TR/∂Q
MC=∂TC/∂Q
Q=25-P
P=25-Q
TR=PQ=25Q-Q²
MR=25-2Q
TC=25+Q+5Q²
MC=1+10Q
25-2Q=1+10Q
12Q=24
Q=24/12=2
P=25-Q=25-2=23
TR=PQ=23•2=46
TC=25+2+5•2²=47
Profit=TR-TC=46-47=-1 (loss)