49 The daily cost in dollars to produce x Sasquatch Berry Pi

49. The daily cost, in dollars, to produce x Sasquatch Berry Pies C(x) = 3x + 36, x 0 and the price-demand function, in dollars per pie, is p(x) = 12 0.5x, 0 x 24.

Solution

C(x) = 3x + 36

price demand , p(x) = 12 - 0.5x

Revenue function , R(x) = x*p(x) = 12x - 0.5x^2

Profit function , P(x) = R(x) - C(x) = -0.5x^2 +12.5x - 12

maximum profit occurs at vertex : x = -b/2a = -(12.5/2*-0.5) = 12.5 berries

maximum profit P(12.5) = -0.5(12.5)^2 + 12.5*12.5 -12 = $ 66.125