Solve the problem.
-The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 350$. Find the number of pretzels that must be sold to maximize profit.
A) $0.8$ pretzels
B) $- 30$ pretzels
C) 800 pretzels
D) 400 pretzels

Question

Quizplus · Accepted Answer

The profit function is a quadratic equation in the form $ax^2 + bx + c$, where $a = -0.002$, $b = 1.6$, and $c = -350$. The maximum profit occurs at the vertex of the parabola, which is given by $x = -\frac{b}{2a}$. Substituting the values, $x = -\frac{1.6}{2(-0.002)} = 400$.

Solve the Problem xxx Pretzels Is Given by the Function P(x)=−0.002x2+1.6x−350P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 350P(x)=−0.002x2+1.6x−350

Solve the Problem $x$ Pretzels Is Given by the Function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 350$