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)=0.2x^2-100x+31,146.what is the minimum unit cost.

Answer 1

18,646

Explanation:

>you can graph the equation on a calculator and see that the minimum is at the point (250, 18646) , so the minimum unit cost is 18,646

>you can use the first derivative to find the minimum

c'(x) = (0.2x²-100x+31,146)' = .4x -100

.4x-100= 0 , so x= 250

c(x=250) = 0.2(250)² -100*250 +31,146 =18,646