Solve the problem
-The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.004 x ^ { 2 } + 2.4 x - 400$. Find the number of pretzels that must be sold to maximize profit.
A) 600 pretzels
B) $1.2$ pretzels
C) 300 pretzels
D) $- 40$ pretzels

Question

Quizplus · Accepted Answer

The profit function $P(x) = -0.004x^2 + 2.4x - 400$ 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 number of pretzels that maximizes profit occurs at the vertex of the parabola. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$. Here, $a = -0.004$ and $b = 2.4$, so $-\frac{2.4}{2(-0.004)} = 300$. Therefore, to maximize profit, the vendor must sell 300 pretzels.

Solve the Problem -The Profit That the Vendor Makes Per xxx

Solve the Problem
-The Profit That the Vendor Makes Per $x$