SOLUTION: A company manufactures lighting fixtures finds its daily production costs to be: C(x) = .25x²-10x+800 dollars for x fixtures produced daily. Find the minimum daily production cost

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Question 446816: A company manufactures lighting fixtures finds its daily production costs to be:
C(x) = .25x²-10x+800 dollars for x fixtures produced daily. Find the minimum daily production cost to the company.

I've set it up:
-> +.25x%5E2-10x%2B800=0+
simplified:
-> +x%5E2-40%2B3200=0+

However, I'm not sure if this is the right way to go with this problem.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+C%28x%29+=+x%5E2+-+40x+%2B+3200+
You don't need to set C%28x%29+=+0
That's only if you want the roots
The minimum of the curve is at +x+=+-b%2F%282a%29+
when the form is +ax%5E2+%2B+2b+%2B+c+=+0+
+-b%2F%282a%29+=+-%28-40%29%2F%282%2A1%29+
+-b%2F%282a%29+=+20+
This is 20 fixtures daily
Now I find C%2820%29
+C%2820%29+=+20%5E2+-+40%2A20+%2B+3200+
+C%2820%29+=+400+-+800+%2B+3200+
+C%2820%29+=+2800+
The minimum daily production cost is $2,800
Here's the plot:
+graph%28+500%2C+500%2C+-10%2C+50%2C+-500%2C+3600%2C+x%5E2+-+40x+%2B+3200%29+