The monthly demand function for a product sold by a monopoly is
p = 3750 − 1/3x^2 dollars, and the average cost is C = 1000 + 70x + 3x^2
dollars. Production is limited to 1000 units and x is in hundreds of units.
(a) Find the quantity that will give maximum profit.
(b) Find the maximum profit. (Round your answer to the nearest cent.)