The monthly demand function for a product sold by a monopoly is p = 2196 1 3 x2 dollars, and the average cost is C = 1000 + 20x + x2 dollars. Production is limited to 1000 units and x is in hundreds of units.

(a) Find the quantity (in hundreds of units) that will give maximum profit. hundred units

(b) Find the maximum profit. (Round your answer to the nearest cent.) $