Question

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?

Answer 1

$11988

Explanation:

Given that,

The unit cost is given by :

`C(x)=0.7x^2-462x+88218`

We need to find the minimum unit cost.

For minimum cost,

Put
`(dC)/(dx)=0`

So,

`(d)/(dx)(0.7x^2-462x+88218)=0\\\\1.4x-462=0\\\\x=(462)/(1.4)\\\\x=330`

Put x = 330 in equation (1).

`C(330)=0.7(330)^2-462(330)+88218\\\\=\$11988`

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