SOLUTION: A chain store manager has been told by the main office that the daily profit, P, is related to the number of clerks working that day,x, according to the function P = -25x^2 + 3

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Question 691277: A chain store manager has been told by the main office that the daily profit, P, is related to the number of clerks working that day,x, according to the function
P = -25x^2 + 300x
What number of clerks will maximize the profit, and what is the maximum possible profit?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The minus in front of the +x%5E2+ term
means there is a max and not a min.
+P+=+-25x%5E2+%2B+300x+
+P+=+x%2A%28+300+-+25x+%29+
Set +P=0+ to find roots
the roots are
+x+=+0+
---------
+300+-+25x+=+0+
+25x+=+300+
+x+=+12+
-----------
The x-coordinate of the maximum
is midway between the roots
+%28+0+%2B+12+%29+%2F+2+=+6+
So +x+=+6+ is the maximum
Now find P at +x=6+
+P+=+-25%2A6%5E2+%2B+300%2A6+
+P+=+-900+%2B+1800+
+P+=+900+
With 6 clerks working that day, there is
a maximum profit of $900
here's a plot:
+graph%28+400%2C+400%2C+-2%2C+15%2C+-50%2C+1000+%2C+-25x%5E2+%2B+300x+%29+