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Unformatted text preview: MA 167 Group Work - 9 Group Name _________________________ Members ________________________ ________________________ ________________________ ________________________ Assignment due Friday, 11/13/09 Optimization 1. Cylindrical cans with circular tops and bottoms are to be manufactured to contain a given volume. There is no waste involved in cutting the tin that goes into the vertical side of the can. But the two circular end pieces are cut from a sheet, as shown at the bottom of the page. If the circles for the tops and bottoms of the cans are fit as snugly as possible, each uses up a hexagonal area of tin, as shown. First, find the area of one of the hexagons in terms of r. (Hint: It consists of 6 equilateral triangles.) Now find the ratio of height to radius for the most economical cans. In other words, minimize the total area of tin needed to make a can. Increasing/Decreasing Functions 2. The population of wolves and caribou in an isolated Alaskan valley are modeled by the equations:...
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- Spring '09