2. Optimization problem The average cost per unit when producing x units of a commodity is given by the equation 1,600+200x+4x³/2 C(x) 0 ≤ x ≤ 1,000 = C(x) in dollars. Find the production level that will minimize the average cost and determine the minimum average cost. Write your answer in full sentence form and include appropriate units. (Be sure to show that what you are finding is indeed a minimum)

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 6SC: A company that makes and sells baseball caps has found that the total monthly cost C in dollars of...
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2. Optimization problem
The average cost per unit when producing x units of a commodity is given by the equation
1,600+200x+4x3/2
C(x)
0≤x≤ 1,000
=
x
C(x) in dollars.
Find the production level that will minimize the average cost and determine the minimum average cost.
Write your answer in full sentence form and include appropriate units. (Be sure to show that what you are
finding is indeed a minimum)
Transcribed Image Text:2. Optimization problem The average cost per unit when producing x units of a commodity is given by the equation 1,600+200x+4x3/2 C(x) 0≤x≤ 1,000 = x C(x) in dollars. Find the production level that will minimize the average cost and determine the minimum average cost. Write your answer in full sentence form and include appropriate units. (Be sure to show that what you are finding is indeed a minimum)
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