Use a graphing utility to graph the function and then answer the question.
-John owns a hotdog stand. He has found that his profit is represented by the equation $P = - x ^ { 2 } + 54 x + 73$ , with P being profits and x the number of hotdogs. How many hotdogs must he sell to earn the most profit?
A) 46 hotdogs
B) 27 hotdogs
C) 28 hotdogs
D) 23 hotdogs

Question

Quizplus · Accepted Answer

The equation $P = -x^2 + 54x + 73$ is a quadratic equation in the form of $ax^2 + bx + c$, where the coefficient of $x^2$ is negative, indicating a downward-opening parabola. The vertex of this parabola gives the maximum point, which is the point of maximum profit for John. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$. Here, $a = -1$ and $b = 54$, so the x-coordinate is $-\frac{54}{2(-1)} = 27$. Therefore, John must sell 27 hotdogs to earn the most profit.

Use a Graphing Utility to Graph the Function and Then P=−x2+54x+73P = - x ^ { 2 } + 54 x + 73P=−x2+54x+73

Use a Graphing Utility to Graph the Function and Then $P = - x ^ { 2 } + 54 x + 73$