SOLUTION: A manufacturer of telephones determines that the profit from producing and selling x telephones is P(x) = -.01x 2 + 6x – 500 dollars. a. How many telephones should be produced to m

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Question 1056798: A manufacturer of telephones determines that the profit from producing and selling x telephones is P(x) = -.01x 2 + 6x – 500 dollars. a. How many telephones should be produced to maximize the profit? b. What is the maximum profit? (This is an application of derivatives)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There is a formula for finding the peak when
the equation looks like
+f%28x%29+=+ax%5E2+%2B+b%2Ax+%2B+c+, it is:
+x%5Bmax%5D+=+-b%2F%282a%29+
+x%5Bmax%5D+=+-6%2F%282%2A%28-.01%29%29+
+x%5Bmax%5D+=+6%2F.02+
+x%5Bmax%5D+=+300+
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You can also find the derivative of +P%28x%29+
and set it to zero to find the peak.
The derivative of +P%28x%29+ is:
+-.02x+%2B+6+=+0+
+-.02x+=+-6+
+x+=+6%2F.02+
+x+=+300+
---------------------
Selling 300 telephones maximizes profit