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A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of machines made. If X machines are made, then the unit cost is given by the function C(x)=0.7x^2-462x+88218 .

What is the minimum unit cost?

Respuesta :

Answer:

$11988

Step-by-step explanation:

Given that,

The unit cost is given by :

[tex]C(x)=0.7x^2-462x+88218[/tex]

We need to find the minimum unit cost.

For minimum cost,

Put [tex]\dfrac{dC}{dx}=0[/tex]

So,

[tex]\dfrac{d}{dx}(0.7x^2-462x+88218)=0\\\\1.4x-462=0\\\\x=\dfrac{462}{1.4}\\\\x=330[/tex]

Put x = 330 in equation (1).

[tex]C(330)=0.7(330)^2-462(330)+88218\\\\=\$11988[/tex]

So, the minimum unit cost is equal to $11988.

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