An aircraft factory manufactures airplane engines. The unit cost (the cost in dollars to make each airplane engine) depends on the number of engines made. If engines are made, then the unit cost is given by the function . What is the minimum unit cost? Do not round your answer.

Incomplete question

Complete question:

An aircraft factory manufactures airplane engines. The unite cost C ( the cost in dollars to make each airplane engine) depends on the number of engines made. If x is the number of engines made, then the unit cost is given by the function C(x)=0.8x^2-160x+26848. What is the minimum unit cost? not rounded

$18848

Explanation:

Since we have the function

C(x) = 0.8x²-160x+26,848

Firstly, we differentiate

C'(x) = 1.6x - 160

The minimum cost will occur where x = 100.

The vertex of a parabola (quadratic equation) occurs where X = -b/2a, in this case we have that

X = 160/(2×0.8) = 100

Therefore, we substitute x = 100 into the original equation

We have that

C(x) = 0.8(100)²-160(100)+26848

C(x) = 8000-16000+26848

C(x) = $18848

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