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 of $ ax^2 + bx + c $. The maximum profit occurs at the vertex of the parabola, which is given by $ x = -\frac{b}{2a} $. Here, $ a = -0.002 $ and $ b = 1.6 $. So, $ x = -\frac{1.6}{2 \times -0.002} = 400 $.

Solve the Problem 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 $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 350$