MCM: The Mathematical Contest in Modeling 2003 MCM Problems PROBLEM A: The stunt Person 问题A:特技人 An exciting action scene in a movie is going to be filmed, and you are the stunt coordinator! 要拍摄一部电影中的令人兴奋的表演场景,而你是特级表演的合作者 A stunt person on a motorcyde will jump over an elephant and land in a pile of cardboard boxes to cushion their fall 骑摩托车的特技人将要跳跃一头大象后落到能使他软着陆的一堆纸箱中, You need to protect the stunt person, and also use relatively few cardboard boxes(lower cost, not seen by camera, etc. 你需要保护特技人,但是还使用相对少的纸箱(降低成本,不被摄象机摄到等。) Your job is to determine what size boxes 确定要使用的箱子的尺寸 determine how many boxes to use 确定要使用多少箱子 determine how the boxes will be stacked 确定要如何堆放箱子 determine if any modifications to the boxes would help 确定如果对箱子做修改的话是否能有帮助, generalize to different combined weights(stunt person motorcycle) and different jump heights 推广到不同的组合重量(特技人与摩托车)和不同的跳跃高度 Note that, in"Tomorrow Never Dies", the James bond character on a motorcycle jumps over a helicopter. 注意,在“明日帝国”, the james bond character骑着摩托车跳过一架直升飞机 PROBLEM B: Gamma Knife Treatment PlanningMCM: The Mathematical Contest in Modeling 2003 MCM Problems PROBLEM A: The Stunt Person 问题 A： 特技人 An exciting action scene in a movie is going to be filmed, and you are the stunt coordinator! 要拍摄一部电影中的令人兴奋的表演场景，而你是特级表演的合作者。 A stunt person on a motorcycle will jump over an elephant and land in a pile of cardboard boxes to cushion their fall. 骑摩托车的特技人将要跳跃一头大象后落到能使他软着陆的一堆纸箱中。 You need to protect the stunt person, and also use relatively few cardboard boxes (lower cost, not seen by camera, etc.). 你需要保护特技人，但是还使用相对少的纸箱（降低成本，不被摄象机摄到等。） Your job is to: • determine what size boxes to use 确定要使用的箱子的尺寸 • determine how many boxes to use 确定要使用多少箱子 • determine how the boxes will be stacked 确定要如何堆放箱子 • determine if any modifications to the boxes would help 确定如果对箱子做修改的话是否能有帮助， • generalize to different combined weights (stunt person & motorcycle) and different jump heights 推广到不同的组合重量（特技人与摩托车）和不同的跳跃高度 Note that, in "Tomorrow Never Dies", the James Bond character on a motorcycle jumps over a helicopter. 注意，在“明日帝国”，the James Bond character 骑着摩托车跳过一架直升飞机。 PROBLEM B: Gamma Knife Treatment Planning