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 the equation P= -25x^2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit?

Answer 1

if you know Calculus ....
dP/dx = -50x + 300 = 0 for a max of P
x = 6
P= -25(36) + 300(6) = 900

otherwise complete the square ....

P = -25(x^2 - 12x + 36-36)
= -25( (x-6)^2 - 36)
= -25(x-6)^2 + 900

same as above