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 functionc(x)=0.6x^2-108x+19,222. What is the minimum unit co

Answer 1

14362

Explanation:

in order to find the minimum unit cost, it is necessary to find the minimum no of machines to be produced. which can be determined by the formula

`x=-(b)/(2a)`

on comparing the given quadratic equation with the standard quadratic equation (i.e
`ax^(2) +bx+c`) we can say that

a = 0.6, b=-108 c= 19222

now
`x= -((-108))/(2(0.6))`

hence x = 90,

now for minimum unit cost, place x= 90 in the given equation

f(90)= 0.6(90)^2-108*(90) +19222

f(90)= 14362