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?

May 20, 2017

30

Explanation:

As the coefficient of ${x}^{2}$ is negative the general form of this graph is $\cap$. Thus it has a maximum

Note that maximum occurs at the vertex.

Write as: $- 1 \left({x}^{2} + \frac{60}{- 1} x\right) + 70$

Using part of the method for completing the square:

${x}_{\text{vertex}} = \left(- \frac{1}{2}\right) \times \frac{60}{- 1} = + 30$