Question 133462
This is a quadratic equation of the form {{{y=ax^2+bx+c}}} and the graph of this relationship is a parabola.  In this case a = -25, b = 300, and c = 0.


Since you put this question in the Algebra: Quadratic Equations section, I'll show you the algebra method to solve it.  If you actually need the calculus method, write back and I'll show you that way.


A parabola with a lead coefficient that is less than zero opens downward, hence the vertex of the parabola is a maximum point.  The x-coordinate of the vertex of a parabola of the form {{{y=ax^2+bx+c}}} is given by {{{(-b)/2a}}} and the y-coordinate is just the value of the function evaluated at the x-coordinate.


For your function, the vertex is at the point (x,y) where


{{{x=(green(-300))/2(green(-25))=red(6)}}} and


{{{y=f(red(6))=-25(6)^2+300(6)=-900+1800=900}}}


So, the maximum profit will be achieved when 6 clerks are working, and that profit is 900 (anybody's guess as to whether that is dollars, thousands of dollars, euros, yen, or some other currency)


Following is a graphical illustration of the situation:


{{{drawing(600,600,-1,13,-10,1000,
grid(1),
graph(600,600,-1,13,-10,1000,-25x^2+300x)
)}}}