SOLUTION: If P(x)=1+8x-2x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit? _________

Algebra ->  Linear-equations -> SOLUTION: If P(x)=1+8x-2x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit? _________       Log On


   

Question 1177769: If P(x)=1+8x-2x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit? _________
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29=1%2B8x-2x%5E2
max is at vertex
complete square and find coordinates of the vertex
P%28x%29=-2x%5E2%2B8x%2B1
P%28x%29=-2%28x%5E2-4x%29%2B1
P%28x%29=-2%28x%5E2-4x%2B2%5E2%29-%28-2%29%282%5E2%29%2B1
P%28x%29=-2%28x-2%29%5E2%2B8%2B1
P%28x%29=-2%28x-2%29%5E2%2B9
=> h=2+and k=9
vertex is at (2,9)
so, x=2 which means 2000 Boombotix speakers should be sold to maximize profit