SOLUTION: John owns a hotdog stand. his profit is represented by P(x)=-x^2+14x+54, with P(x) being profit and the x the number of hotdogs sold. What is the most he can earn?

Question 168495: John owns a hotdog stand. his profit is represented by P(x)=-x^2+14x+54, with P(x) being profit and the x the number of hotdogs sold. What is the most he can earn?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
P(x)=-x^2+14x+54
Looking at the coefficient associated with the x^2 we see that it is negative. This means that the vertex is the max.
.
The axis of symmetry is the line x = -b/2a
x = -b/2a
x = -14/2(-1)
x = -14/(-2)
x = 7
.
Solving the equation P(x) when x=7:
P(x)=-x^2+14x+54
P(7)=-7^2+14(7)+54
P(7)=-49+98+54
P(7)=-49+152
P(7)= $103

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