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Unformatted text preview: Optimal Mushroom Harvest ESM 242 April 2, 2007 1 Problem Setup My friend Jay is a farmer in the Goleta Hills. About this time of year, Jay harvests wild mushrooms on his farm. But every year Jay faces the dilemma of how many mushrooms to harvest. The tension is as follows: He’d like to harvest more mushrooms this year (because he will make more money), but the more he harvests this year, the smaller will be the stock of mushrooms next year (and so he will make less money in the future). This is a very typical problem of natural resource extraction. There are basically two ways of solving problems like this. The first is to estimate the relationships and parameters for Jay’s farm, plug them into a computer, and derive a solution for Jay. The second approach is to try to solve this problem generally , so that we can apply the solution to other problems. We’ll solve Jay’s problem both ways here. 2 Mushroom harvest model Let X t be the biomass of mushrooms on Jay’s farm in year t . The new growth of mushrooms as a function of the current mushroom population is given by the function F ( X t ). The harvest of mushrooms is...
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 Spring '07
 COSTELLO
 Optimization, Jay, Xt

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