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2015年美国数学建模竞赛第二次模拟赛题A题


Problem A

Warmer Days or Sour Grapes ?

The high quality of wines(葡萄酒) produced in the Finger Lakes Region(五指湖 区) of upstate (北部)New York is widely known. Proximity(接近) to lakes tempers the climate and makes it more suitable for growing several varieties of premium (独特) grapes: Riesling (雷司令) , Gewü rztraminer (琼瑶浆) , Chardonnay (霞多丽), Merlot(梅洛), Pinot Noir(黑比诺), and Cabernet Franc(品丽珠). (There are many more, but we will restrict(限制) the discussion to these six to simplify(简化) the modeling.) Each variety has its own preferred “average temperature” range but is also different in its susceptibility (感受性) to diseases and ability to withstand(抵抗) short periods of unusually cold temperature. As our local climate changes, the relative suitability of these varieties will be changing as well. A forward-looking winery (酒厂) has hired your team to help with the long-term planning. You will need to recommend a) the proportion (比例) of the total vineyard (葡萄园) to be used for growing each of the above six varieties; b) and when should these changes be implemented (实施)(based on observed temperatures and/or current market prices for each type of wine). Naturally, the winery is interested in maximizing its annual profit. But since the latter (后者)is weather-dependent, it might vary a lot year-to-year. You are also asked to evaluate the trade-offs (权衡)between optimizing the expected/average case versus the worst(-realistic-)scenario(情景). Things to keep in mind: (复杂) and predicting the rate of “global warming” is a hotly debated area. For the purposes of this problem, assume that the annual average temperature in Ithaca(伊萨卡), NY will increase by no more than 4° C by the end of this century. average temperature – a short snap(临时) of sub-zero (零度) temperature in late Ferburay or early March (after the vines already started getting used to warmer weather) is far more damaging than the same low temperature would be in the middle of the winter. start producing grapes suitable for winemaking.


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