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# L27 - material 6 A swimmer is 100 meters from a straight...

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L27 – Optimization Problems Procedure: 1. Write down the given information and conditions and what you wish to ﬁnd 2. Sketch and assign symbols to known and unknown quantities 3. Write the quantity to be maximized or minimized and if needed, express it as a function of one variable 4. Use calculus to solve 1

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Find two positive numbers whose product is a maximum if the sum of the ﬁrst and twice the second is 100. 2
A farmer wishes to fence the adjacent ﬁelds below with 1200 ft of fencing. What is the maximum area he can enclose? 3

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Find the coordinates of the point on the curve y = x 2 closest to the point (2 , 1 2 ). 4
Find the area of the largest right triangle that can be formed as shown between the x -axis and the curve y = 9 - x 2 . 5

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An open box with a square bottom is to be constructed with a volume of 108 cubic feet. Find the dimensions of the box that will require the least amount of

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Unformatted text preview: material. 6 A swimmer is 100 meters from a straight shore. A lifeguard is 300 meters from the point on the shore closest to the swimmer. If he/she can swim at 3 m/sec and run at 5 m/sec, what path will get him/her to the swimmer as fast as possible? 7 A cylindrical tube is to be constructed of heavy cardboard with plastic ends having a volume of 48 π cubic feet. What radius will minimize the cost of the tube if cardboard is \$1 per square foot and plastic is \$3 per square foot? 8 A cylinder is inscribed in a sphere of radius 4 inches. Find the height of the cylinder of maximum volume that can be formed this way. 9 A court is to be built as a rectangle with a semicircle at each end. If the perimeter is to be 1200 feet, what dimensions will maximize the enclosed area? 10...
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L27 - material 6 A swimmer is 100 meters from a straight...

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