handout_11_04 - speed of 6 m/s Jill will row across the...

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MATH 1A: OPTIMIZATION 1. A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle θ . How should θ be chosen to maximize the amount of water carried by the gutter? 2. The sum of two numbers is 20. What is the minimum possible value of the sum of their squares? 3. You are the designer of a coke can. Your job is to find the dimensions of a cylindrical can that holds 2 π fl oz of coke and minimizes heat loss, which is proportional to the surface area. What are the optimal dimensions? Date : November 4, 2009. 1
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4. Find the points on the ellipse 4 x 2 + y 2 = 4 that are furthest away from the point (1 , 0). 5. Jack and Jill are going to have a race on a circular pond. Jack will run around the circumference at a
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Unformatted text preview: speed of 6 m/s. Jill will row across the water at a speed of 3 m/s. How should Jack choose the starting and ending points of the race to win by as large a margin as possible? 6. A boat leaves a dock at 2:00 PM and travels due south at a speed of 20 km/hr. Another boat has been heading due east at 15 km/hr and reaches the same dock at 3:00 PM. At what time were the two boats closest together? 7. A Norman window has the shape of a semicircle on top of a rectangle. If the perimeter of the window is 30 ft, find the dimensions of the window so that the greatest possible amount of light is admitted. 2...
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