If the total revenue function for a blender is $R ( x ) = 35 x - 0.25 x ^ { 2 },$ determine how many units x must be sold to provide the maximum total revenue in dollars.
A)1225
B)3000
C)35
D)200
E)70

Question

Quizplus · Accepted Answer

The maximum total revenue occurs at the vertex of the parabola represented by the given quadratic function. The x-coordinate of the vertex can be found using the formula $x = -\frac{b}{2a}$ for a quadratic function in the form $ax^2 + bx + c$. Here, $a = -0.25$ and $b = 35$, so $x = -\frac{35}{2(-0.25)} = 70$.

If the Total Revenue Function for a Blender Is R(x)=35x−0.25x2,R ( x ) = 35 x - 0.25 x ^ { 2 },R(x)=35x−0.25x2,

If the Total Revenue Function for a Blender Is $R ( x ) = 35 x - 0.25 x ^ { 2 },$