SOLUTION: Giselle wants to run a tutoring program over the summer. She comes up with the following profit function: P(x)=-2x^2+100x=25 where x represents the price of the program. Between w

Algebra ->  Equations -> SOLUTION: Giselle wants to run a tutoring program over the summer. She comes up with the following profit function: P(x)=-2x^2+100x=25 where x represents the price of the program. Between w      Log On


   

Question 1107128: Giselle wants to run a tutoring program over the summer. She comes up with the following profit function: P(x)=-2x^2+100x=25 where x represents the price of the program. Between what two prices should she charge to make a profit? How much should she charge her students if she wants to make the most profit?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The function is -2x^2+100x-25=0, and positive is profit.
Can graph it
graph%28300%2C300%2C-15%2C70%2C-200%2C1500%2C-2x%5E2%2B100x-25%29
Need zeros to show the range of values
multiplying by -1 get 2x^2-100x+25=0
x=(1/4)(100+/-sqrt(10000-200); sqrt(9800)=98.99
x=(1/4)(198.99)=49.75 and x=(1/4)(1.01) or 0.25, round to $0.26, exact is $0.2525.
Maximum is at vertex. and x=-b/2a=-100/4=$25
Between $0.25 and $49.75, maximum at $25.