Question 864999
{{{P=-25x^2+300x}}}, daily profit for x clerks.


Finding the maximum P.
Factor the definition.
{{{P=-25(x^2-12x)}}}
{{{P=-25x(x-12)}}}
The maximum will happen in the middle of the x intercept values, so solve for these using {{{-25x(x-12)=0}}}.
x-intercepts are 0 and 12.


The midpoint of 0 and 12 is {{{highlight(x=6)}}}, for the maximum P.
Evaluate P for x=6.