Medical equipment x ray machines

Asked by maham237 @ 06/01/2021 in Mathematics viewed by 317 People

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?

Do not round your answer

Answered by maham237 @ 06/01/2021

Answer:

Minimum Unit Cost = $14,362

Step-by-step explanation:

The standard form of a quadratic is given by:

ax^2 + bx + c

So for our function, we can say,

a = 0.6

b = -108

c = 19,222

We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a

So,

-(-108)/2(0.6) = 108/1.2 = 90

Plugging this value into original function would give us the minimum (unit cost):

$c(x)=0.6x^2-108x+19,222\\c(90)=0.6(90)^2-108(90)+19,222\\=14,362$

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