John owns a hotdog stand. He has found that his profit is represented b the equation #P= -x^2 +60x +70#, with P being profits and x the number of hot dogs. How many hotdogs must he sell to earn the most profit?

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Answer 1 · 2017-05-20T13:15:30

30

As the coefficient of #x^2# is negative the general form of this graph is #nn#. Thus it has a maximum

Note that maximum occurs at the vertex.

Write as: #-1(x^2+60/(-1)x)+70#

Using part of the method for completing the square:

#x_("vertex")=(-1/2)xx60/(-1)=+30#

Tony B