What is the minimum unit cost? Do not round answer.

Question

A aircraft factory manufactures airplane engines. The unit cost C(the cost in dollars to make each airplane engine) depends on the amount of engines made. If X engines are made, then they unit cost is given by the function C(x)=0.8x^2-512x+93,451. What is the minimum unit cost? Do not round your answer.

Answer 1

C(x) = .8x^2 -512x + 93,451

take the derivative, set equal to zero, solve for x, then plug back into C(x)

C'(x) = 1.6x -512 = 0

x = 512/1.6 = 320

C(320) = .8(320)^2 - 512(320) + 93,451 = 81920 - 163,840 + 93,451 = $11,531= min per unit cost

(that's the exact answer, not rounded)