Question 2375
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 {{{-25(6)^2 + 300*6}}}

max profit = 900

jon