《运筹学》复习题.doc

《运筹学》复习题.doc1工商12《运筹学》复习题一、求解下列线性规划:???????????????????0,,16284204242242max32132121321321xxxxxxxxxxxxxxz解:标准型为(用M法求解):????????????????????????0,,,,16284204242242max73216321521743217321xxxxxxxxxxxxxxxxMxxxxz?BCBXb211000-Mi?1x2x3x4x5x6x7x-M7x4[4]22-1001105x2024001001006x1648200104-z4M4M+22M+12M+1-M00021x111/21/2-1/4001/405x1803-11/210-1/23606x12060[1]01-112-z-20001/200-M-1/221x4121/2001/4005x1200-101-1/2-104x12060101-1-z-80-3000-1-M2所以,8,)0,0,12,12,0,0,4(**??zXT。二、已知线性规划模型????????????????????无约束321321321321321,0,101632182635maxxxxxxxxxxxxxxxxz的最优解为TX)4,0,14(*??,试用对偶理论求其对偶问题的最优解。解:其对偶模型为:????????????????????无约束321321321321321,0,633252101618minyyyyyyyyyyyyyyyw因为014*1??x,所以52*3*2*1???yyy又因为18102*3*2*1????xxx,所以0*1?y根据**wz?,有46101618*3*2*1???yyy解上述三个联立方程得:3,1,0*3*2*1???yyy三、求解下列指派问题:(要求给出所有最优解)?????????????????????6864434656738665)(min444141ijijijijcxcz解:????????????????????????????????????????????????141000031330210024201013234031106864434656738665***3???????????????0300000402202101最优方案为?????????????????????????????000101001000001010000***********或X最优值为18*?z。四、某生产线单独生产一种产品的能力为36000件/年,对该产品的需求速度为18000件/年,。准备在生产线上轮流生产多种产品,更换生产品种时,需准备结束费500元/次。假设不允许缺货,求该产品每次最佳的生产批量。解:依题意,有P=36000件/年,R=18000件/年,次元/5003?C,年件元./?C件)(4472)1800036000(?????????RPPCRCQ五、求解下列运输问题:(使总运费最低)运价销地产地1B2B3B产量1A422102A214103A32310销量8910解:用最小元素法确定初始运输方案如下:运价销地产地1B2B3B*B产量1A42723010/72A1291