A company sells 3000 sets of headphones per month when the price is $70 per set. If the price is reduced to $40 per set, 6000 sets are sold. The monthly cost of producing x sets is C(x) = 55,000 + 30x. Find a) the number of sets to sell to maximize profit. b) the max profit c) the price of a set of headphones when the profit is maximized.