Would some body help me with this question?

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)=0.6x^2-108x+19,222. What is the minimum unit cost?

Answer 1

Find the minimum value by this formula

x = -b / 2a which gives you the x coordinate of the vertex. Replace x with this value and solve for the y coordinate which is the minimum value.

108/2(.6)

x = 90

The number of machines that will minimize the cost. Plug this value into the original equation to get the cost.

Answer 2

To find the minimum of a function, you have to look for critical points- this is done by setting the first derivative equal to zero.

c(x) = 0.6x^2-108x+19,222

Then c'(x) = 1.2x - 108

Setting c'(x) = 0

1.2x=108

x= 90 machines

This is the number of machines that will minimize the cost per machine.

Plugging this into the cost function:

c(90)=0.6(90^2)–108(90)+19222 = $14362