Explanation Given: The cost function is C ( x ) = 200 + 50 x − 50 ln x ; x ≥ 1 . Calculation: Consider the cost function C ( x ) = 200 + 50 x − 50 ln x . The average cost function is C ¯ ( x ) = C ( x ) x . Substitute C ( x ) = 200 + 50 x − 50 ln x in C ¯ ( x ) = C ( x ) x , C ¯ ( x ) = 200 + 50 x − 50 ln x x = 200 x + 50 − 50 ln x x Thus, the average cost function is C ¯ ( x ) = 200 x + 50 − 50 ln x x . Evaluate C ¯ ′ ( x ) as follows. C ¯ ′ ( x ) = d d x ( 200 x + 50 − 50 ln x x ) = 200 ( − 1 x 2 ) − 50 ( ln x ( − 1 x 2 ) + 1 x ( 1 x ) ) = − 200 x 2 − 50 ( − ln x x 2 + 1 x 2 ) = − 200 + 50 ln x − 50 x 2 = 50 ln x − 250 x 2 Thus, C ¯ ′ ( x ) = 50 ln x − 250 x 2

COLL.MATH F/BUS ECO.(LL+18 WEEK MYLAB E)

14th Edition

ISBN: 9780135998083

Author: Barnett

Publisher: PEARSON

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Chapter 11, Problem 63RE

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To find: The minimum average cost.

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Chapter 11, Problem 62RE

Chapter 11, Problem 64RE

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COLL.MATH F/BUS ECO.(LL+18 WEEK MYLAB E)

Ch. 11.1 - Matched Problem 1 Repeat Example 1 for f(x) = x2 –...Ch. 11.1 - Matches Problem 2 Find the critical numbers of f,...Ch. 11.1 - Matched Problem 3 Find the critical numbers of f,...Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 7MP Ch. 11.1 - Prob. 8MP Ch. 11.1 - Prob. 9MP Ch. 11.1 - Skills Warm-up Exercises In Problems 1-8, inspect...

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