SOLUTION: A company determines that the cost C, in dollars of producing x tennis rackets is C= 32x+120,000. the revenue R in dollars, from selling all of the tennis racquets is R = x(200-0.0

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Question 32563: A company determines that the cost C, in dollars of producing x tennis rackets is C= 32x+120,000. the revenue R in dollars, from selling all of the tennis racquets is R = x(200-0.01x).
How many rackets should the company manufacture and sell if the company wishes to earn a profit of at least $550.000?
Solution:
-0.01x^2+168x-670,000is >or= to 0
It says use the quadratic formula to find the approximate values of the inequality, but I keep coming up with a -under the radical sign and can't solve it. Can someone write out what I am doing wrong w/ finding the approximate values? The approximate critical values are supposed to be 6513.2 and 10,286.8, so the company should manufacture at least 6514 racquets but not more than 10,286 to produce the desired proffit. I am lost on how they are getting this answer.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I'll put your quadratic into the automatic solution software
this site provides to see what it comes up with.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.01x%5E2%2B168x%2B-670000+=+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=%28168%29%5E2-4%2A-0.01%2A-670000=1424.

Discriminant d=1424 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-168%2B-sqrt%28+1424+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28168%29%2Bsqrt%28+1424+%29%29%2F2%5C-0.01+=+6513.20377358868
x%5B2%5D+=+%28-%28168%29-sqrt%28+1424+%29%29%2F2%5C-0.01+=+10286.7962264113

Quadratic expression -0.01x%5E2%2B168x%2B-670000 can be factored:
-0.01x%5E2%2B168x%2B-670000+=+-0.01%28x-6513.20377358868%29%2A%28x-10286.7962264113%29
Again, the answer is: 6513.20377358868, 10286.7962264113. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.01%2Ax%5E2%2B168%2Ax%2B-670000+%29


Hope that helps.
Cheers,
Stan H.