Maximum profit. 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 function P = −25x2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit? Step by step answers please.
This is the equation of a parabola that opens downwards (because the coefficient of x2 is negative) so the maximum value of P will be found at the parabola's vertex.
The x-coordinate of the vertex is given by: -b
Your equation is already in the standard form: (a = -25, b = 300, c = 0) so we can find the x-coordinate at which P will be the maximum.
- 300 = -300 = 6 So six clerks will maximize the profit.
To find the maximum profit, plug 6 into the equation for X
P = -25 (6)2 + 300(6)
= -25 (36) + 1800
= -900 + 1800
= 900 this is the maximum profit