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Marginal Cost, Revenus, and Profit for Producing LED TVs The weekly demand for the Pulsar 25 color LED television is represented by p, where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. p = 550 - 0.07x (0 5 x 5 12,000) The weekly total cost function associated with manufacturing the Pulsar 25 is given by C(x), where C(x) denotes the total cost (in dollars) incurred in producing x sets. Find the following functions (in dollars) and compute the following values. C(x) = 0.000001x - 0.02x2 + 470x + 75,000 (a) Find the revenue function R. R(x ) = Find the profit function P. P ( X) = (b) Find the marginal cost function C'. C' ( x ) = Find the marginal revenue function R'. R' ( x ) = Find the marginal profit function P'. P' (x ) = (c) Compute the following values. (Round your answers to two decimal places.) C'(2,500) = R'(2,500) = P'(2,500) = (d) Sketch C(x). 2.0 x 106 2000 4000 6000 8000 10 000 12 000 -2x 10 1.5 x 106 -4x106 1.0 x 106 -6x 10 -8x 106 500 000 O-1x10' X AO 2000 4000 6000 8000 10 00012 000 -1x106 2000 4000 6000 8000 10 000 12 000 4x 106 -2x 106 3x 106 -3x106 -4x106 2x 106 -5x 106 1 x 106 -6x106 O-7x 106 2000 4000 6000 8000 10 000 12 000 Sketch R(x). R R 1.5 x 107 5x 106 5x 106 1.0 x 10' 4x 106 3x 106 5.0 x 106 2x 106 1x 106 O 2000 4000 6000 8000 10 00012 000 -X 2000 4000 6000 8000 10 000 12 000 R 1 x 106 -2x 106 2000 4600 6000 8000 10 000 12 000 2000 4000 6000 8006 10 000 12 000 -1x106 4x106 -2x 106 6x 106 -3x 106 -8x 106 70-1x10 Sketch P(x). 8x 106 800 000 600 000 6x 106 100 000 4x 10 200 000 2x 106 2000 4000 6000 8000 10 000 12 000 2000 4000 6000 8000 10 000 12 000 P 0.002 2000 4000 6000 8000 10 000 12 000 2000 4006 6000 8000 10 000 12 000 -0.004 -2x 106 -0.006 4x 106 -0.008 -0.010 -6x 106 O-0.012 10-8x106 (i)