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An Aircraft factory manufactures airplane engines. The unit cost C ( the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made, then the unit cost is given by the function C(x)=0.6^2-324x+56,258. What is the minimum unit cost? Do not round your answer.

An Aircraft factory manufactures airplane engines The unit cost C the cost in dollars to make each airplane engine depends on the number of engines made If x en class=

Respuesta :

We have that the unit cost is given by a parabola, and the leading coefficient is given by 0.6 (it is positive), then, we have a minimum in the shape of the parabola.

A way to find the minimum is to find the vertex of the parabola (in this given case, the vertex is the minimum point) which coordinates are as follows:

[tex]x_v=-\frac{b}{2a},y_v=c-\frac{b^2}{4a}[/tex]

Since we need to find the minimum unit cost, we need to find the value for y. Then, we have:

[tex]0.6x^2-324x+56258[/tex]

a = 0.6

b = -324

c = 56258

Then

[tex]y_v=56258-\frac{(-324)^2}{4\cdot(0.6)}\Rightarrow y_v=12518[/tex]

Therefore, the minimum unit cost is equal to $12,518.

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