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A firm has an average cost function  A(q) = 125/q+q^2/16 where  a is the firm's output.  Determine the level of output for average costs are minimum  Hence the determine the range of values for which average costs are decreasing  What part of the decreasing range is practically feasible  Write an equation for the total cost function  Hence calculate the level of output for which total cost costs are minimum

A firm has an average cost function  A(q) = 125/q+q^2/16 where  a is the firm's output.  Determine the level of output for average costs are minimum  Hence the determine the range of values for which average costs are decreasing  What part of the decreasing range is practically feasible  Write an equation for the total cost function  Hence calculate the level of output for which total cost costs are minimum

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section: Chapter Questions
Problem 26MCQ
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A firm has an average cost function  A(q) = 125/q+q^2/16 where  a is the firm's output. 

Determine the level of output for average costs are minimum 

Hence the determine the range of values for which average costs are decreasing 

What part of the decreasing range is practically feasible 

Write an equation for the total cost function 

Hence calculate the level of output for which total cost costs are minimum

Expert Solution
1) answer

Given average cost function is:

Aq=125q+q216

The minimum value of the average cost is found where dAdq=0

dAdq=0⇒125-1q2+2q16=0⇒q3=103⇒q=10

Therefore, the level of output for average cost is minimum is for q=10

2) answer

The average cost decreases for the values for which ddqAq<0

dAdq<0⇒125-1q2+2q16<0⇒q3<103⇒q<10

Therefore, the average cost decreases for the values when q<10

The range of values practically feasible is: 0<q<10

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