Solve the problem.
-The profit that the vendor makes per day by selling x pretzels is given by the function $$P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150$$ Find the number of pretzels that must be sold to maximize profit.
A)400 pretzels
B)170 pretzels
C)800 pretzels
D)0.8 pretzels

Question

Quizplus · Accepted Answer

The profit function $P(x) = -0.002x^2 + 1.6x - 150$ 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, given by the formula $x = -\frac{b}{2a}$, represents the number of pretzels sold to maximize profit. Substituting $a = -0.002$ and $b = 1.6$ into the formula gives $x = -\frac{1.6}{2(-0.002)} = 400$. Therefore, to maximize profit, the vendor must sell 400 pretzels.

Solve the Problem P(x)=−0.002x2+1.6x−150P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150P(x)=−0.002x2+1.6x−150

Solve the Problem $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150$