SOLUTION: John owns a hotdog stand. He has found that his profit is represented by the equation P(x)=-x^2+64x+72, with P being profits and x the number of hotdogs sold. How many hotdogs must

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: John owns a hotdog stand. He has found that his profit is represented by the equation P(x)=-x^2+64x+72, with P being profits and x the number of hotdogs sold. How many hotdogs must      Log On


   

Question 607844: John owns a hotdog stand. He has found that his profit is represented by the equation P(x)=-x^2+64x+72, with P being profits and x the number of hotdogs sold. How many hotdogs must he sell to earn the most profit?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Using the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex

P(x)=-x^2+64x+72 = -(x-32)^2+ 1024 + 72  |completing the Square

P(x)=-(x-32)+ 1096 |Parabola opening downward, Pt(32,1096)maximum

earn the most profit when x = 32