求助2011全国大学生数学建模D题答案，十分感激！D题 天然肠衣搭配问题？谢谢
推荐回答（1个）
D题 天然肠衣搭配问题
天然肠衣（以下简称肠衣）制作加工是我国的一个传统产业，出口量占世界首位。肠衣经过清洗整理后被分割成长度不等的小段（原料），进入组装工序。传统的生产方式依靠人工，边丈量原料长度边心算，将原材料按指定根数和总长度组装出成品（捆）。
原料按长度分档，通常以0.5米为一档，如：3-3.4米按3米计算，3.5米-3.9米按3.5米计算，其余的依此类推。表1是几种常见成品的规格，长度单位为米，∞表示没有上限，但实际长度小于26米。
表1 成品规格表
最短长度 最大长度 根数 总长度
3 6.5 20 89
7 13.5 8 89
14 ∞ 5 89
为了提高生产效率，公司计划改变组装工艺，先丈量所有原料，建立一个原料表。表2为某批次原料描述。
表2 原料描述表
长度 3-3.4 3.5-3.9 4-4.4 4.5-4.9 5-5.4 5.5-5.9 6-6.4 6.5-6.9
根数 43 59 39 41 27 28 34 21
长度 7-7.4 7.5-7.9 8-8.4 8.5-8.9 9-9.4 9.5-9.9 10-10.4 10.5-10.9
根数 24 24 20 25 21 23 21 18
长度 11-11.4 11.5-11.9 12-12.4 12.5-12.9 13-13.4 13.5-13.9 14-14.4 14.5-14.9
根数 31 23 22 59 18 25 35 29
长度 15-15.4 15.5-15.9 16-16.4 16.5-16.9 17-17.4 17.5-17.9 18-18.4 18.5-18.9
根数 30 42 28 42 45 49 50 64
长度 19-19.4 19.5-19.9 20-20.4 20.5-20.9 21-21.4 21.5-21.9 22-22.4 22.5-22.9
根数 52 63 49 35 27 16 12 2
长度 23-23.4 23.5-23.9 24-24.4 24.5-24.9 25-25.4 25.5-25.9
根数 0 6 0 0 0 1
根据以上成品和原料描述，设计一个原料搭配方案，工人根据这个方案“照方抓药”进行生产。
公司对搭配方案有以下具体要求：
(1) 对于给定的一批原料，装出的成品捆数越多越好；
(2) 对于成品捆数相同的方案，最短长度最长的成品越多，方案越好；
(3) 为提高原料使用率，总长度允许有± 0.5米的误差，总根数允许比标准少1根；
(4) 某种规格对应原料如果出现剩余，可以降级使用。如长度为14米的原料可以和长度介于7-13.5米的进行捆扎，成品属于7-13.5米的规格；
(5) 为了食品保鲜,要求在30分钟内产生方案。
请建立上述问题的数学模型，给出求解方法，并对表1、表2给出的实际数据进行求解，给出搭配方案。
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