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 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
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.