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John owns a hot dog stand. He has found that his profit is represented by the equation p(x)=-x^2+62x+77, with p being profits and x the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Respuesta :

altavistard
We want to maximize the profit, p(x) = -x^2 + 62x + 77.  
The graph of this function is a parabola that opens down.  The x-coordinate of the vertex is x = -b/(2a), which here is x = -62 / (2*-1), or 31.  So, we'll maximize John's profit if we advise him to sell 31 hot dogs.

He will have to sell 31 hot dogs to get the most profits.

p(x) = -x² + 62x + 77

where

p = profits

x = number of hot dogs

Therefore,

To earn the highest profit is where is at the maximum. Therefore, using vertex formula.

x = - b / 2a

where

a = -1

b = 62

Therefore,

x = - 62 / -2

x = 31

We can say his max profit occurs when he sell 31 hot dogs.

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