If the total revenue function for a blender is , find the maximum revenue if production is limited to at most 150 blenders.
A)$4,000
B)$200
C)$40
D)$3,750
E)$150

Question

If the total revenue function for a blender is  , find the maximum revenue if production is limited to at most 150 blenders. ​
A)$4,000 
B)$200 
C)$40 
D)$3,750 
E)$150

Quizplus · Accepted Answer

To find the maximum revenue, we need to find the vertex of the quadratic function. The revenue function is given by R(x) = -0.02x^2 + 15x, where x is the number of blenders produced. The coefficient of the x^2 term is negative, so the quadratic opens downwards, which means that the vertex is a maximum point.

The x-coordinate of the vertex is given by x = -b/2a, where a and b are the coefficients of the x^2 and x terms, respectively. In this case, a = -0.02 and b = 15, so x = -15/(2*(-0.02)) = 375.

Since we are limited to producing at most 150 blenders, we can only sell 150 blenders at the most. Therefore, the maximum revenue is R(150) = -0.02(150)^2 + 15(150) = $3,750. Therefore, the answer is D.

If the Total Revenue Function for a Blender Is