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

Answer:

$11988

Step-by-step 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 $\dfrac{dC}{dx}=0$

So,

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

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.