SOLUTION: maximum profit a chain store manager has been told by the main office that the daily profit P is related to the number of clerks working that day, x, according to the equation p=-2

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Question 80109: maximum profit a chain store manager has been told by the main office that the 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 maxamize the profit, and what is the maximum possible profit?
are they wanting us to solve as a equation i am confused please give me step by step instructions so I can complete the rest of my problems am freaking out
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
maximum profit a chain store manager has been told by the main office that the 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 maxamize the profit, and what is the maximum possible profit?
:
p = -25x^2 + 300x is a quadratic equation so you can find the the max profit by
finding the x value of the axis of symmetry and find the vertex with that:
:
Axis of symmetry formula: x = -b/(2a)
In equation; p = -25x^2 + 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 = -25(6^2) + 300(6)
p = -25(36) + 1800
p = -900 + 1800
p = $900 is the actual profit
:
A profit/clerk graph will look like this:
+graph%28+300%2C+200%2C+-4%2C+15%2C+-100%2C+1000%2C+-25x%5E2+%2B+300x%29+
:
Notice the max occurs when x = 6 clerks which is the axis of symmetry and
the vertex is the max profit of 900