1、 运筹学教程（第二版）习题解答运筹学教程第一章习题解答1.1用图解法求解下列线性规划问题。并指出问题具有惟一最优解、无穷多最优解、无界解还是无可行解。min Z 2x 3x2 max Z 3x 2x21 14x 6x 6 2x x 21st. 2x 2x 412 1st. 3x 4x 121x , x 012(1) (2)2 2x1, x 02 2max Z x x2 max Z 5x 6x21 16x 10x 120 2x x 21st. 5 x 102 1st. 2x 3x 212(3) (4) 1 2 5 x 82x1, x 0 2page 26 January 2011 School
2、of Management运筹学教程第一章习题解答min Z 2x 3x214x 6x 61 2(1) st.2x 2x 41x1, x 02 2无穷多最优解，1x1 1, x , Z 3是一个最优解2 3max Z 3x 2 x 212 x x 2 1 2st . 3x 4 x 12(2) 1 2x , x 01 2该问题无解page 36 January 2011 School of Management运筹学教程第一章习题解答max Z x x216x 10x 1201st. 5 x 102(3) 15 x 8 2唯一最优解， x 10, x 6,Z 161 2max Z 5x 6x21
3、 2x x 21st. 2x 3x 21x1, x 02(4) 22该问题有无界解page 46 January 2011 School of Management运筹学教程第一章习题解答1.2 将下述线性规划问题化成标准形式。min Z 3x 4x 2x 5x41 2 34x x 2x x 21 2 3 4x x x x 141 2 3 2x 3x x x 2.1 2 3 4x , x , x 0, x 无约束24(1) st 1 2 3 4min Z 2 x 2 x 3x31 2 x x x 41 2 3(2) st 2 x x x 61 2 3x 0, x 0, x 无约束 1 2 3p
4、age 56 January 2011 School of Management运筹学教程第一章习题解答minZ 3x 4x 2x 5x41 2 34x x 2x x 21 2 3 4 2 14 .x x x x (1) 1 2 3 4st2x 3 x x 2 1 2 3 4x ,x ,x 0,x无约束1 2 3 4max Z 3x 4x 2x 5x 5x421 2 3 41 4x x 2x x x 21x1 x x 2x 2x x 14 2x 3x x x x x 22 3 41 42 2 3 41 42 5st 1 2 3 41 42 6 x1, x , x , x , x , x 02
5、3 41 42 6page 66 January 2011 School of Management运筹学教程第一章习题解答min Z 2x 2x 3x31 2 x x x 41 2 3(2) st 2x x x 61x 0, x 0, x无约束2 3 1 2 3max Z 2x 2x 3x 3x321 2 31 x x x x 41st 2x x x x x 62 31 32 1 2 31 32 4 x1, x , x , x , x 02 31 32 4page 76 January 2011 School of Management运筹学教程第一章习题解答1.3 对下述线性规划问题找出所
6、有基解，指出哪些是基可行解，并确定最优解。max Z 3x x 2x31 212 x 3x 6x 3x 918x x 4x 2x 102 3 4(1) 1 2 3 5st 3x x 0 1 6x 0（, j 1, ,6）jmin Z 5x 2x 3x 2x41x 2x 3x 4x 72st 2x 2x x 2x 32 33 1 4(2) 1 2 3 4x 0,( j 1, 4) jpage 86 January 2011 School of Management运筹学教程第一章习题解答max Z 3x x 2x31 212 x 3x 6x 3x 918x x 4x 2x 102 3 4(1)
7、1 2 3 5st 3x x 0 1 6x 0（, j 1, ,6）j基可行解x10x23x30x40 3.5 0x5 x6 Z3300 0 1.5 0 85000 0 00300.75 0 2 2.25 2.25page 96 January 2011 School of Management运筹学教程第一章习题解答min Z 5x 2x 3x 2x41x 2x 3x 4x 72st 2x 2x x 2x 32 33 1 4(2) 1 2 3 4x 0,( j 1, 4) j基可行解x10x20.50x32x40Z50 1 1 52/5 0 11/5 0 43/5page 106 January 2011 School of Management
