SOLUTION: It cost Acme Manufacturing C dollars per hour to operate its golf ball division. An analyst has determined that C is related to the number of golf balls produced per hour, x, by t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: It cost Acme Manufacturing C dollars per hour to operate its golf ball division. An analyst has determined that C is related to the number of golf balls produced per hour, x, by t      Log On


   

Question 23342: It cost Acme Manufacturing C dollars per hour to operate its golf ball division. An analyst has determined that C is related to the number of golf balls produced per hour, x, by the equations C = 0.009x^2 - 1.8x + 100. What number of balls per hour should Acme produce to minimize the cost per hour of manufacturing these golf balls?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Cost is a quadratic equation with a=0.009, b=-1.8, c=100
The max or min is at x=-b/2a = 1.8/0.018 = 100
You need to produce 100 golf balls per hour.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.009x%5E2%2B-1.8x%2B100+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1.8%29%5E2-4%2A0.009%2A100=-0.359999999999999.

The discriminant -0.359999999999999 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -0.359999999999999 is + or - sqrt%28+0.359999999999999%29+=+0.6.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.009%2Ax%5E2%2B-1.8%2Ax%2B100+%29


Cheers,
Stan H.