Question

Word problem involving the maximum or minimum DA 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 ofmachines made. If x machines are made, then the unit cost is given by the function ()=0,21 -724+ 17,791. What is the sinimum unit costoDo not round your answer

Answer 1

The standard form of a quadratic is given by:

ax^2 + bx + c

So for our function, we can say,

a = 0.2

b = -72

c = 17791

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

So:

-(-72)/(2*0.2) = 180

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

C(x) = 0.2x^2 - 72x + 17791

C(180) = 0.2(180^2) - 72*180 + 17791 = 11311