Help with economics question?

Question

Q= Quantity = 500 - Price so P = Price = 500 - Q. There is a fixed cost of 30,000 and a marginal cost of 100 *Q. Please help me find max price and quantity. My hunch is that

Max Price = 496
Max Quantity = 4
Profit = 1984

Answer 1

P= 500-Q
P= (30000+100Q)/Q
(500-Q)Q=30000+100Q
Q²-500Q+100Q+30000=0
Q²-400Q+30000=0
Solve to get solution