SOLUTION: The cost C (in dollars) of manufacturing x wheels at Deon's Bicycle Supply is given by the function C(x)= 0.1x^2-60x+22,744. What is the minimum cost of manufacturing wheels? Do no

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Question 856622: The cost C (in dollars) of manufacturing x wheels at Deon's Bicycle Supply is given by the function C(x)= 0.1x^2-60x+22,744. What is the minimum cost of manufacturing wheels? Do not round your answer.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+C%28x%29+=+.1x%5E2+-+60x+%2B+22744+
This is a parabola which has a minimum
Here's the plot:
+C%28x%29+ is plotted on the y-axis and
is rescaled to thousands of dollars
+graph%28+500%2C+500%2C+-100%2C+700%2C+-5%2C+30%2C+.0001x%5E2+-+.06x+%2B+22.744+%29+
An initial guess would be +C%5Bmin%5D+=+14000+
---------------------
When the form is:
+a%2Ax%5E2+%2B+b%2Ax+%2B+c+, the min ( or max ) is at
+x%5Bmin%5D+=+-b%2F%282a%29+
+a+=+.1+
+b+=+-60+
+-b%2F%282a%29+=+-%28-60%29+%2F+%282%2A.1%29+
+-b%2F%282a%29+=+60%2F.2+
+x%5Bmin%5D+=+300+
Now plug this value of x back into equation:
+C%28x%29+=+.1x%5E2+-+60x+%2B+22744+
+C%28300%29+=+.1%2A300%5E2+-+60%2A300+%2B+22744+
+C%28300%29+=+9000+-+18000+%2B+22744+
+C%28300%29+=+13744+
The minimum cost is $13,744