College Algebra & Trigonometry, 2018a

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4.9. OPTIMIZATION 245 The graph for this function is below: 25 (2, 24) 20 15 10 5 −1 1 2 3 4 We can see in the graph that the maximum volume given a cost of $72 will be when the base of the box is 2 feet by 2 feet. The volume will be 24 ft 3 and the height will be 6 feet. So the answer to the question is 2 ft × 2ft× 6 ft.
246 CHAPTER 4. FUNCTIONS Exercises 4.9(b) 1) A rectangular storage container with an open top has a volume of 10 m 3 . The length of its base is twice the width. Material for the base costs $10 per square meter. The sides require material that costs $6 per square meter. Find the cost of materials for the cheapest such container. 2) A poster is to contain 108 cm 2 of printed matter, with margins of 6 cm each at the top and bottom of the page and 2 cm on each side of the page. What is the minimum cost of the poster if it is to be made of material which costs $0.20 per square centimeter? 3) If 1200 cm 2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box. 4) A box with a square base and open top must have a volume of 32,000 cm 3 . Find the dimensions of the box that minimizes the amount of material used. 5) A Norman window has the shape of a semi-circle on top of a rectangle so that the diameter of the semi-circle is the same as the width of the rectangle. Given that the perimeter of the window should be 30 ft, find the dimensions of the window that will admit the greatest amount of sunlight (maximize the area). 6) A rectangular box with no top is to be made from material costing $0.50 per square foot. The width of the base is 5 ft and it will have a volume of 6 ft 3 . What
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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10 CHAPTER 1. ALGEBRA REVIEW Exampl
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12 CHAPTER 1. ALGEBRA REVIEW 2(x +3
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40 CHAPTER 1. ALGEBRA REVIEW devise
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88 CHAPTER 2. POLYNOMIAL AND RATION
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100 CHAPTER 2. POLYNOMIAL AND RATIO
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140 CHAPTER 3. EXPONENTS AND LOGARI
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190 CHAPTER 4. FUNCTIONS by substit
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192 CHAPTER 4. FUNCTIONS 4.2 Domain
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306 CHAPTER 7. COMBINATORICS differ
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College Algebra & Trigonometry, 2018a

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