SOLUTION: a chain store manager has been told by the main office that daily profit P is related to the number of clerks working that day. x according to equation P=-25x^2+300x. What number

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Question 2375: a chain store manager has been told by the main office that daily profit P is related to the number of clerks working that day. x according to equation P=-25x^2+300x. What number of clerks will maximize the profit and what is the maximum possible profit?
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
dP/dx = -50x + 300
To find the max (or min), is where the gradient (dp/dx) is zero, so ask that...
0 = -50x + 300
hence x = 6.
Prove it is a max too, by differentiating again...d2P/dx2 = -50. This is -ve therefore MAX
So max number of clerks = 6.
This maximises the profit, P to be
max profit = 900
jon