a. Explanation Given Information: A function that shows the number of paintings sold with in a year is given by N ( c ) = 0.6 c 2 − 54 c + 1230 where c dollars per painting. Graph : Interpretation: The first derivative of the function is given by, N ( c ) = 0.6 c 2 − 54 c + 1230 N ' ( c ) = 1.2 c − 54 N ' ( c ) = 0 1.2 c − 54 = 0 c = 45 The function has a global minimum at c = 45 .This means when the cost per painting is 45 dollars the lowest number of paintings that can be sold per year is 15 . Between c ∈ [ 5 , 55 ] the function has no local maximum point. At the end points of c ∈ [ 5 , 55 ] , N ( c ) = 0.6 c 2 − 54 c + 1230 N ( 5 ) = 0 b. To determine To Find: the revenue function R ( c ) c. To determine To Find: the price per painting to earn most money and the least money d. To determine To Explain: the most amount of money cannot be earned at the same price per painting for which you sell the most paintings.

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 3.4, Problem 61A

To determine

To Graph: greatest and lowest number of paintings and the price

To determine

To Find: the revenue function R(c)

To determine

To Find: the price per painting to earn most money and the least money

To determine

To Explain: the most amount of money cannot be earned at the same price per painting for which you sell the most paintings.

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Chapter 3.4, Problem 60A

Chapter 3.4, Problem 62A

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Chapter 3 Solutions

Calculus

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To Graph: greatest and lowest number of paintings and the price

Solution Summary: The author explains how the function shows the highest and lowest number of paintings and the price. The function has a global minimum and no local maximum.

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To Graph: greatest and lowest number of paintings and the price

To Find: the revenue function R(c)

To Find: the price per painting to earn most money and the least money

To Explain: the most amount of money cannot be earned at the same price per painting for which you sell the most paintings.

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Chapter 3 Solutions