If the total revenue function for a blender is $R ( x ) = 40 x - 0.25 x ^ { 2 },$ find the maximum revenue.
A)$80
B)$1500
C)$40
D)$100
E)$1600

Question

Quizplus · Accepted Answer

The maximum revenue occurs at the vertex of the parabola represented by the revenue function. The vertex $x$ value is found using $-b/(2a)$ for the quadratic $ax^2 + bx + c$. Here, $a = -0.25$ and $b = 40$, so $x = -40/(2 \times -0.25) = 80$. Substituting $x = 80$ into the revenue function gives $R(80) = 40(80) - 0.25(80)^2 = 1600$.

If the Total Revenue Function for a Blender Is R(x)=40x−0.25x2,R ( x ) = 40 x - 0.25 x ^ { 2 },R(x)=40x−0.25x2,

If the Total Revenue Function for a Blender Is $R ( x ) = 40 x - 0.25 x ^ { 2 },$