Solve the problem.
-John owns a hot dog stand. His profit, in dollars, is given by the function $P ( x ) = - x ^ { 2 } + 14 x + 57$, where $x$ is the number of hot dogs sold. What is the most he can earn?
A) $\$ 99$
B) $\$ 120$
C) $\$ 106$
D) $\$ 49$

Question

Quizplus · Accepted Answer

To find the most John can earn, we need to find the vertex of the parabola represented by the profit function. The x-coordinate of the vertex can be found by using the formula: $-b/2a$, where $a = -1$ and $b = 14$. Therefore, the x-coordinate of the vertex is $7$. To find the corresponding y-coordinate, we substitute $x = 7$ into the profit function: $P(7) = -(7)^2 + 14(7) + 57 = 106$. Thus, the most John can earn is $$106$.

Solve the Problem P(x)=−x2+14x+57P ( x ) = - x ^ { 2 } + 14 x + 57P(x)=−x2+14x+57

Solve the Problem $P ( x ) = - x ^ { 2 } + 14 x + 57$