Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar-powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long River’s rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one page summary sheet, prepare a one page memo to the managers of the river describing your key findings. 

 

在大长河野营(美国竞赛2012年B题) 

 

游客到大长河(225英里)可以领略风光和令人兴奋的白色激流。这条河是进不去登山者的, 因此观光只能用的方式是沿河旅行, 这需要几天的露营。所有的沿河旅行都始于第一站并在下游225英里远的最终出口退出。观光者或者乘坐桨动力船只以平均每小时4英里速度旅行, 或者乘坐摩托船以平均每小时8英里旅行。这趟沿河行程可能有6至18个夜晚需在河边露营。政府管理当局负责管理这条河，使得每一个旅行者都可享受一份野营体验, 且在河岸可以最少地接触其他的船只。目前, 在每年在六个月的旅游季节中有 X 个旅行团队沿着大长河旅行, 一年其余部分的天气太冷不适合做这种河流旅行。有 Y 个营地差不多均匀分布在大长河河道两岸上。因为沿河漂流受欢迎程度上升, 有关方要求公园管理者允许更多的旅行团队沿河旅行。他们想确定怎样可以安排一种最优的混合旅行方式, 可以是不同的持续时间(以在河边过夜为单位)和不同的旅行方式进(马达或桨), 可以最大限度地利用好营地。换句话说, 在漂流季节可能容纳多少旅行团队？河流管理者雇用你给他们提供建议，安排一个最佳行程方式和测算河流的承载能力, 记住没有两队露营者在同一时间占据同一露营地点。除了你的一页摘要, 请准备一页备忘录, 对河流管理人员描述你主要的发现。