Posted by Turner on .
You are the manager of a monopoly, and your demand and cost functions are given by P = 300 – 2.5Q and C(Q)=1000 + 2.5Q2.
a.At what price and quantity are firm’s profits maximized?

Managerial Econ 
Steve,
revenue = price * quantity
profit = revenue  cost
so, the profit is
Q(3002.5Q)  (1000 + 2.5Q^2)
= 300Q  2.5Q^2  1000  2.5Q^2
= 5Q^2 + 300Q  1000
= 5(Q^2  60Q + 200)
max profit at Q=30, P(30)=225