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Unformatted text preview: Some Practice Problems for the 1A Final These problems are by no means inclusive of everything you need to know for the final. You should practice many problems for each section of the book that we have covered. This is just a selection of some problems to help you get started with your review for the final. Make sure to give full explanation for every problem! 1. A farmer wants to fence an area of 1 . 5 million square feet in a rectangular fence and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the costs of the fence? 2. 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. 3. Find the point on the line y = 2 x + 1 that is closest to the point (3 , 2). 4. Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible. 5. A metal storage tank with volume V is to be constructed in the shape of a right circular cylinder surmounted by a hemisphere. What dimensions will require the least amount of metal?...
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- Fall '09