SOLUTION: How many award designs must be sold in order to maximize the profit using the following P(x)=-0.4x^2+80x-1600. The teacher is asking me to also show my work algebratically.

Algebra ->  Linear-equations -> SOLUTION: How many award designs must be sold in order to maximize the profit using the following P(x)=-0.4x^2+80x-1600. The teacher is asking me to also show my work algebratically.      Log On


   

Question 800892: How many award designs must be sold in order to maximize the profit using the following P(x)=-0.4x^2+80x-1600. The teacher is asking me to also show my work algebratically.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29=-0.4x%5E2%2B80x-1600
The vertex occurs at x=-b%2F2a. At this value for x, the maximum function value is attained.
x=-b%2F2a
x=-80%2F2%28-0.4%29
x=80%2F0.8
x=100=> x coordinate of the vertex

P%28x%29=-0.4%2A100%5E2%2B80%2A100-1600
P%28x%29=-0.4%2A10000%2B8000-1600
P%28x%29=-4000%2B8000-1600
P%28x%29=2400 => y coordinate of the vertex and represents maximum of the profit
so, vertex is at (100,2400)

+graph%28+600%2C+600%2C+-100%2C+250%2C+-100%2C+2610%2C+-0.4x%5E2%2B80x-1600%29+