SOLUTION: John owns a hot dog stand. He has found that his profit is represented by the equation P = -x2 + 56x + 77, with P being profit in dollars and x the number of hot dogs. Using this

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: John owns a hot dog stand. He has found that his profit is represented by the equation P = -x2 + 56x + 77, with P being profit in dollars and x the number of hot dogs. Using this       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 765848: John owns a hot dog stand. He has found that his profit is represented by the equation P = -x2 + 56x + 77, with
P being profit in dollars and x the number of hot dogs. Using this model, what is the maximum profit that John
can make? How many hot dogs must he sell in order to to obtain that maximum profit?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

P+=+-x%5E2+%2B+56x+%2B+77........this is a parabola; since the coefficient of leading term is -1, parabola turns downward and the vertex will be maximum
so, we need to find the coordinates (h,k) of a vertex
use the formula h+=+-b%2F2a to find the x coordinate h of the vertex of a parabola and k+=+P%28h%29 to find the y coordinate k of the vertex

h+=+-56%2F2%28-1%29
h+=+-56%2F-2
h+=+28...........since h+=+x, this is the number of hot dogs
P%2828%29+=+-28%5E2+%2B+56%2A28+%2B+77
P%2828%29+=-784+%2B+1568+%2B+77
P%2828%29+=861..........since k+=+y, this is maximum profit
so, the vertex is at (h,k)=(28,861)