运筹学(胡运权)第五版课后问题详解,运筹作业..pdf

实用标准47 页 1.1bX2432101234X13x1+4x2=122x1+x2=2用图解法找不到满足所有约束条件的公共范围，所以该问题无可行解47 页 1.1dX254321X12x1-x2=2-2x1+3x2=2-6-5-4-3-2-1-1-21234无界解文案大全实用标准1.2（b）约束方程的系数矩阵A=12342112P1P2P3P4()基基P1P2P1P3P1P4P2P3P2P4P3P4-411/2002/5011/50-1/30011/601/2200-1/2020011是否是否是55基解基解是否可行解是否可行解目标函数值目标函数值X1 X2 X3 X4否43/5最优解 A=(01/220)T 和(0011)T49 页 13 题设 Xij 为第 i 月租 j 个月的面积minz=2800 x11+2800 x21+2800 x31+2800 x41+4500 x12+4500 x22+4500 x32+6000 x13+6000 x23+7300 x14s.t.x11+x12+x13+x1415x12+x13+x14+x21+x22+x2310 x13+x14+x22+x23+x31+x3220 x14+x23+x32+x4112Xij0用 excel求解为：文案大全实用标准用 LINDO求解：LP OPTIMUM FOUND AT STEP3OBJECTIVE FUNCTION V ALUE1)118400.0VARIABLEVALUEREDUCED COSTZ0.0000001.000000X113.0000000.000000文案大全实用标准X210.0000002800.000000X318.0000000.000000X410.0000001100.000000X120.0000001700.000000X220.0000001700.000000X320.0000000.000000X130.000000400.000000X230.0000001500.000000X1412.0000000.000000ROWSLACK OR SURPLUSDUAL PRICES2)0.000000-2800.0000003)2.0000000.0000004)0.000000-2800.0000005)0.000000-1700.000000NO. ITERATIONS=3答 若使所费租借费用最小，需第一个月租一个月租期 300 平方米，租四个月租期 1200 平方米，第三个月租一个月租期 800 平方米，文案大全实用标准50 页 14 题设 a1，a2，a3, a4, a5 分别为在 A1, A2, B1, B2, B3 加工的产品数量，b1，b2，b3分别为在 A1, A2, B1 加工的产品数量，c1 为在 A2，B2上加工的产品数量。

则目标函数为maxz= (1.25-0.25)( a1+a2+a3)+( 2-0.35) b3+( 2.8-0.5)c1 -0.05 (a1+b1)-0.03 (a2+b2+c1)- 0.06 (a3+b3)-0.11(a4+c1)-0.05a5=0. 95a1+0. 97a2+0. 94a3+1.5b3+2.1c1-0.05b1-0.11a4-0.05a5s.t.5a1+10b160007a2+b2+12c1100006a3+8a340004a4+11c170007a54000a1+a2-a3-a4-a5=0b1+b2-b3=0a1，a2，a3, a4, a5, b1，b2，b3, c10用 lindo 求解得：LP OPTIMUM FOUND AT STEP6OBJECTIVE FUNCTION VALUE1)16342.29VARIABLEVALUEREDUCED COSTA11200.0000000.000000A20.0000009.640000A3285.7142940.000000B310000.0000000.000000C10.00000015.900000B10.0000000.230000A4342.8571470.000000A5571.4285890.000000B210000.0000000.000000ROWSLACK OR SURPLUSDUAL PRICES2)0.0000000.1680003)0.0000001.5000004)0.0000000.0750005)5628.5712890.0000006)0.0000000.0085717)0.0000000.1100008)0.000000-1.500000文案大全实用标准NO. ITERATIONS=6计算 lindo 截屏2.1a:2.1a:对偶问题为：maxz=2y1+3y2+5y3s.t.y1+2y2+y323y3+y2+4y324y1+3y2+3y3=4y10, y 20,y3 无约束因为原问题的对偶问题的对偶问题仍是原问题， 因此本问题的对偶问题的对偶问题为：minz=2x1+2x2+4x3s.t.x1+3x2+4x322x1+x2+3x33x1+4x2+3x3=5x1,x20,x3无约束8181 页页 2.122.12文案大全实用标准a)设 x1,x2,x3 分别为 A，B，C 产品数量maxz=3x1+x2+4x3s.t.6x1+3x2+5x3453x1+4x2+5x330 x1,x2,x30用 lomdo 求解为LP OPTIMUM FOUND AT STEP2OBJECTIVE FUNCTION VALUE1)27.00000VARIABLEVALUEREDUCED COSTX15.0000000.000000X20.0000002.000000X33.0000000.000000X1,X2,X30.0000000.000000ROWSLACK OR SURPLUSDUAL PRICES2)0.0000000.2000003)0.0000000.6000004)0.0000000.000000NO. ITERATIONS=2文案大全实用标准最大生产计划为 A生产 5个单位，C 生产 3 个单位b)b)LP OPTIMUM FOUND AT STEPLP OPTIMUM FOUND AT STEP2 2OBJECTIVE FUNCTION VOBJECTIVE FUNCTION VALUEALUE1)1)27.0000027.00000V VARIABLEARIABLEV VALUEALUEREDUCED COSTREDUCED COSTX1X15.0000005.0000000.0000000.000000X2X20.0000000.0000002.0000002.000000X3X33.0000003.0000000.0000000.000000X1,X2,X3X1,X2,X30.0000000.0000000.0000000.000000ROWROWSLACK OR SURPLUSSLACK OR SURPLUSDUAL PRICESDUAL PRICES2)2)0.0000000.0000000.2000000.2000003)3)0.0000000.0000000.6000000.6000004)4)0.0000000.0000000.0000000.000000NO. ITERATIONS=NO. ITERATIONS=2 2RANGES IN WHICH THE BASIS IS UNCHANGED:RANGES IN WHICH THE BASIS IS UNCHANGED:OBJ COEFFICIENT RANGESOBJ COEFFICIENT RANGESV VARIABLEARIABLECURRENTCURRENTALLOWABLEALLOWABLEALLOWABLEALLOWABLECOEFCOEFINCREASEINCREASEDECREASEDECREASEX1X13.0000003.0000001.8000001.8000000.6000000.600000X2X21.0000001.0000002.0000002.000000INFINITYINFINITYX3X34.0000004.0000001.0000001.0000001.5000001.500000X1,X2,X3X1,X2,X30.0000000.0000000.0000000.000000INFINITYINFINITYRIGHTHAND SIDE RANGESRIGHTHAND SIDE RANGESROWROWCURRENTCURRENTALLOWABLEALLOWABLEALLOWABLEALLOWABLERHSRHSINCREASEINCREASEDECREASEDECREASE2 245.00000045.00000015.00000015.00000015.00000015.0000003 330.00000030.00000015.00000015.0000007.5000007.5000004 40.0000000.0000000.0000000.000000INFINITYINFINITY文案大全实用标准可知 A产品的利润变化范围【6. 8,2.4】,上述计划不变。

c) c)设设 x4x4 为产品为产品 D D 的数量的数量maxz=3x1+x2+4x3+3x4s.t.6x1+3x2+5x3+8x48x4453x1+4x2+5x3+2x430 x1,x2,x3 ,x40用 lomdo 求解为LP OPTIMUM FOUND AT STEPLP OPTIMUM FOUND AT STEP0 0OBJECTIVE FUNCTION VOBJECTIVE FUNCTION VALUEALUE1)1)27.5000027.50000文案大全实用标准V VARIABLEARIABLEV VALUEALUEREDUCED COSTREDUCED COSTX1X10.0000000.0000000.1000000.100000X2X20.0000000.0000001.9666671.966667X3X35.0000005.0000000.0000000.000000X4X42.5000002.5000000.0000000.000000ROWROWSLACK OR SURPLUSSLACK OR SURPLUSDUAL PRICESDUAL PRICES2)2)0.0000000.0000000.2333330.2333333)3)0.0000000.0000000.5666670.566667NO. ITERATIONS=NO. ITERATIONS=0 0安排生产安排生产 D D 有利，新最有生产计划为有利，新最有生产计划为 x1=x2=0,x3=5,x4=2.5x1=x2=0,x3=5,x4=2.5，利润为，利润为 27.527.5d)maxz=3x1+x2+4x3-0.4ys.t.6x1+3x2+5x3453x1+4x2+5x3-y30 x1,x2,x3,y0用 lomdo 求解为LP OPTIMUM FOUND AT STEPLP OPTIMUM FOUND AT STEP0 0OBJECTIVE FUNCTION VOBJECTIVE FUNCTION VALUEALUE文案大全实用标准1)1)30.0000030.00000V VARIABLEARIABLEV VALUEALUEREDUCED COSTREDUCED COSTX1X10.0000000.0000000.6000000.600000X2X20.0000000.0000001.8000001.800000X3X39.0000009.0000000.0000000.000000Y Y15.00000015.0000000.0000000.000000ROWROWSLACK。