Question

5. 12 points HarMathAp11 10.3.019 My Notes Ask Your Teacher If the total cost function for a product is C(x) = 240(0.02x + 5)3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost? units Find the minimum average cost per unit. Submit Answer Save Progress 6. -12 points HarMathAp11 10.3.025 My Notes Ask Your Teacher If the profit function for a product is P(x) = 2700x + 120x2-x3-242,000 dollars, selling how many items, x, will produce a maximum profit? items Find the maximum profit.

Answer 1

C (x) = 240 (0.02x + 5)^3 Average Cost function bar C (x) = C (x)/x = 240 (0.02x + 5)^3 we need to find critical point d bar c (x)/dx = 240 (0.06x (0.02x + 5)^2 - (0.02x + 5)^3/x^2) plug d bar c (x)/dx = 0 (240) (0.06x (0.02x + 5)^2 - (0.02x + 5)^3 = 0 (0.06x - (0.02x + 5)) = 0 0.02x + 5 = 0 Rightarrow x = -250 0.06x = 0.02x + 5 0.04x = 5 x = 500/4 = 125, 125 Here for -250 < x < 125 C' (x) > 0 for infinity > x > 125 C' (x) < 0 so x = 125 is point minimum 125 units (will minimize average cost) plug x = 125