For the average cost function A(q)=3q+5+ 75/q determine the level of production for which the...

Question:

For the average cost function

{eq}A(q)=3q+5+ \frac{75}{q}{/eq}

determine the level of production for which the average cost is minimized.

Minimum of a function:

The minimum of a function is where the function takes its lowest value. We can find the point where the function takes its minimum value through differentiation. This is how we solve this question.

We can find the number of units that minimize the average cost by equating the derivative of the average cost function to zero and solving for x.

{eq}A(q)=3q+5+ 75/q\\ \displaystyle A'(q)=3-\frac{75}{q^2}\\ A'(q)=0\\ \displaystyle \Rightarrow 3=\frac{75}{q^2}\\ q=5 {/eq}

Thus, the average costs are minimized when 5 units are produced.

Minimum Values: Definition & Concept

from

Chapter 18 / Lesson 16
145K

The minimum value of a quadratic function is the low point at which the function graph has its vertex. This lesson will define minimum values and give some example problems for finding those values. A quiz will complete the lesson.