SOLUTION: I have no clue on what to do in order to solve this problem. I have tried numerous times and it doesnt seem like it is right. can someone help please? Maximum profit. A chain st

Question 642364: I have no clue on what to do in order to solve this problem. I have tried numerous times and it doesnt seem like it is right. can someone help please?
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 = -25x^2 +300x. What number of clerks will maximize the profit, and what is the maximum possible profit?
Found 2 solutions by solver91311, lwsshak3:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The graph of your profit function is a convex down parabola because of the negative lead coefficient. Hence, the vertex of the parabola is a maximum. You need the coordinate of the vertex to answer your question. The -coordinate of the vertex of the parabola is given by . Just plug in your given values for and and then do the arithmetic.

John

My calculator said it, I believe it, that settles it

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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 = -25x^2 +300x. What number of clerks will maximize the profit, and what is the maximum possible profit?
**
P = -25x^2 +300x.
This is an equation of a parabola that opens downwards (has a maximum).
Its standard form: y=-A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex
y-coordinate of vertex=maximum value
problem, then, is to find coordinates of the vertex
..
For given problem:
P = -25x^2 +300x.
complete the square
P = -25(x^2-12x+36)+900
P=-25(x-6)^2+900
vertex: (6,900)
maximum possible profit=900

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