Firm S is the only producer of a particular type of foam fire retardant and insulation used in the construction of commercial buildings. The inverse demand equation for the product is
P = 1,500 - .1Q,
Where Q is the annual sales quantity in tons and P is the price per ton.
The firm’s total cost function (in dollars) is
C = 1,400,000 + 300Q + .05Q2.
a. To maximize profit, how much foam insulation should firm S plan to produce and sell? What price should it charge?
b. Compute the firm’s total profit.