College of education mathematics department
CHAPTER 5: APPLICATIONS OF INEQUALITIES
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CHAPTER 5: APPLICATIONS OF INEQUALITIES5.1. Applications of Cauchy inequalityExercise 5.1. Give a square aluminum plate 6 cm. People want to cut a trapezoid like a drawing. Solution: Find the sum of so that the area of the trapezoid EFGH reaches the minimum value. We have . To the scale up EFGH reaches the minimum value, then reaches the maximum value. We have . Put (1). On the other hand we have (2). Substituting (2) into (1) we have . We have the largest S when is the smallest . When then . Therefore, . Exercise 5.2. During the peak tourist season, a hotel complex in Da Nang with 100 rooms at the same price is always full when the rent is 480 thousand VND/room. Through the survey in previous years, the motel's sales department found that: for every increase in room price by compared to when the room was full (rental price was 480 thousand VND/room), the number of rooms for rent decreased by . Ask the motel to list the room rate is how much to achieve the highest revenue? Solution: The number of rooms for rent when the room price increases x% is: Corresponding total revenue: We have (thousand VND) The sign " =" occurs when The listed room price is: 480+4,8.12,5=540 (thousand VND) Exercise 5.3. Mr. Quang wants to build a water surface in the shape of a rectangular box with a lid with a capacity of 3000 liters. The bottom surface is a rectangle whose length is twice its width. The cost of hiring labor to build the lake is VND 500000 per square meter. What is the minimum cost Mr. An needs to spend to build a water tank? Solution: Let x be the width of the tank, the length of the tank is 2x ⇒ the area of the bottom is . Since the tank volume is the tank height is . Construction area is the total area of the tank is So the building area is at least when . The minimum construction cost is VND. tải về 344.73 Kb. Chia sẻ với bạn bè của bạn:
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