Question

5. The price Plin $) and the quantity x sold of a certain product obey the demand equation ( X -5p + 100 0s p s 20 ix) XP) A) Express the revenue R as a function of x: R(x) 8) What is the revenue if 15 units are sold C) What quantity x maximizes revenue? What is the maximum revenue? D) What price should the company charge to maximizes revenue

Answer 1

X = -5P + 100 5P = -X + 100 P = -X/5 + 20 r = P TIMES X = (- X/5 + 20) X r = - X^2/5 + 20X r(15) = -X^2/5 + 20X r(15) = -15^2/5 + 20 TIMES 15 = 255 in this parabolic equation R = -x^2/5 +{ 20x a = -1/5, b = 20 maximize x = -b/20 = -20/2(2/5) x_max = + 50 max revenue R(50) = -50^2 + 20 times 50 = 1500 P = - x/5 + 20 for x = 50 = -50/5 + 20 = 10