The monthly demand function for x units of a product sold by a monopoly is p = 5,700 – x2 dollars, and its average cost is C = 3,020 + 2x dollars. Production is limited to 100 units. Find the revenue function, R(x), in dollars. R(x) = 1 5700x Find the cost function, C(x), in dollars. C(x) = 3020x + 2x Find the profit function, P(x), in dollars. 3 – 2x2 + 2680x P(x) Find P'(x). 3 2 P'(x) = 4x + 2680 2 Find the number of units that maximizes profits. (Round your answer to the nearest whole number.) 49.80 X units Find the maximum profit. (Round your answer to the nearest cent.) $ 66738.50 Does the maximum profit result in a profit or loss? profit loss

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