A medical equipment industry manufactures X-ray machines. HELP :)

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
=Cx+−0.9x2594x112,620
. What is the minimum unit cost?

Answer 1

This looks like a quadratic function. I believe it is something like C(x) = 0.9x² - 594x + 112600.

If this is the correct function, then what we are being asked to do is to find the absolute minimum. To find this, we look to the coefficients (numbers in front of the variables). In the general form of ax² + bx + c, we take -b/2a.

594/2(.9) = 330. This means we would need to make 330 x-ray machines to get our minimum cost. But what is the cost when 330 x-ray machines are made?

To find out, we must evaluate the function for 330.

C(330)= 0.9(330)² - 594(330) + 112600

=98010 - 196020 + 112600

=$14,590

Supposing I guessed the signs correctly, the minimum cost would be $14,590. If they make less or more than 330 x-ray machines, the cost will go up.

Keep in mind that the price above is for 330 units. We must divide by 330 to find the minimum cost for 1 unit.

14590/330= $44.22

The minimum cost per unit will be approximately $44.22.

I am guessing a bit as far as what the original equation is supposed to be, but I hope this helps in understanding how to find maximum or minimum values for quadratic functions.