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)=x²-680x+127,958. How many machines must be made to
minimize the unit cost?
Do not round your answer.
Number of X-ray machines:
X
5

Answer 1

:

To find the number of machines that must be made to minimize the unit cost, we need to find the minimum value of the function C(x). To do this, we can take the derivative of C(x) and set it equal to zero:

C'(x) = 2x - 680

2x - 680 = 0

x = 340

Therefore, the minimum value of C(x) occurs when x = 340, and 340 machines must be made to minimize the unit cost.