Max Profit

In: Film and Music

Submitted By jerwolfe
Words 301
Pages 2
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?
This is a quadratic equation with a negative coefficient of x2, so I know that the max is on the axis of symmetry. The formula for the axis of symmetry; x = -b/ (2a), in this equation a = -25, b = 300 X = - 300 / 2 • (-25) I will simplify the equation: p = -25x2 + 300x quadratic equation Therefore you can find the max profit by finding the value of x of the axis of symmetry and find the vertex with that: Axis of symmetry formula: x = -b/ (2a) In equation; p = -25x2 + 300x a = -25 b = 300 x = -300/ (2)-25 x = -300/ -50 x = 6 clerks will maximize the profit To find the max profit, substitute 6 for x in the original equation:
P =-252+300x=0
P = -25(62) + 300(6) Substitute 6 for x.
P = -25(36) + 1800 factor both left and right side.
P = -900 + 1800 add to solve equation.
P = $900 is the actual profit

A profit/clerk graph will look like this: The basic shape of the graph in this equation of a parabola that opens downwards (coefficient of x2 is negative) so the maximum value of P will be found at the parabola's vertex. The parabola will cross the x axis at 0 and 6.
To maximize profits, the manager should employ 6 clerks. The maximum profit can be found by substituting 6 for x in the original equation for P. The graph represents the maximum number of clerks needed to gain the maximum daily…...

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