Economics—Marginal Analysis: The EZ-Craft Company determines that the price-demand function, in dollars, for their new U-Make-It picture frame is , with a cost function of C(x) = 60x + 72,000, where x represents the number of frames produced and C(x) represents the cost in dollars.
(a) Determine the revenue function R.
(b) Determine the profit function P. Find the smallest and largest production levels x so that the company realizes a profit. Do this by determining the smallest and largest x-values so that R(x) > C(x).
(c) Evaluate P′(3000) and interpret.
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