Solve the problem.
-The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 300$. Find the number of pretzels that must be sold to maximize profit.
A) 400 pretzels
B) 800 pretzels
C) $0.8$ pretzels
D) 20 pretzels

Question

Quizplus · Accepted Answer

The profit function $P(x) = -0.002x^2 + 1.6x - 300$ 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 profit. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$. Here, $a = -0.002$ and $b = 1.6$, so $-\frac{1.6}{2(-0.002)} = 400$. Therefore, 400 pretzels must be sold to maximize profit.

Solve the Problem xxx Pretzels Is Given by the Function P(x)=−0.002x2+1.6x−300P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 300P(x)=−0.002x2+1.6x−300

Solve the Problem $x$ Pretzels Is Given by the Function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 300$