运筹学习题集二

运筹学习题集二

习题一

1.1 用法求解下列线性规划问题并指出各问题是具有唯一最优解、无穷多最优解、无界解或无可行解。

(1) min z =6x1+4x2 (2) max z =4x1+8x2 st. 2x1+ x2≥1 st. 2x1+2x2≤10 3x1+ 4x2≥1.5 -x1+ x2≥8 x1, x2≥0 x1, x2≥0

(3) max z = x1+ x2 (4) max z =3x1-2x2 st. 8x1+6x2≥24 st. x1+x2≤1 4x1+6x2≥-12 2x1+2x2≥4 2x2≥4 x1, x2≥0 x1, x2≥0

(5) max z=3x1+9x2 (6) max z =3x1+4x2 st. x1+3x2≤22 st. -x1+2x2≤8 -x1+ x2≤4 x1+2x2≤12 x2≤6 2x1+ x2≤16 2x1-5x2≤0 x1, x2≥0

x1, x2≥0

1.2. 在下列线性规划问题中找出所有基本解指出哪些是基本可行解并分别代入目标函数比较找出最优解。

(1) max z =3x1+5x2 (2) min z =4x1+12x2+18x3 st. x1 + x3 =4 st. x1 +3x3- x4 =3

2x2 + x4 =12 2x2+2x3 - x5=5 3x1+ 2x2 + x5 =18 xj ≥0 (j=1,…,5) xj ≥0 (j=1,…,5)

1.3. 分别用法和单纯形法求解下列线性规划问题并对照指出单纯形法迭代的每一步相当于法可行域中的哪一个顶点。 (1) max z =10x1+5x2 st. 3x1+4x2≤9 5x1+2x2≤8 x1, x2≥0

(2) max z =100x1+200x2 st. x1+ x2≤500 x1 ≤200 2x1+6x2≤1200 x1, x2≥0

1.4. 分别用大M法和两阶段法求解下列线性规划问题并指出问题的解属于哪一类:

(1) max z =4x1+5x2+ x3 (2) max z =2x1+ x2+ x3 st. 3x1+2x2+ x3≥18 st. 4x1+2x2+2x3≥4 2x1+ x2 ≤4 2x1+4x2 ≤20 x1+ x2- x3=5 4x1+8x2+2x3≤16 xj ≥0 (j=1,2,3) xj ≥0 (j=1,2,3)

(3) max z = x1+ x2 (4) max z =x1+2x2+3x3-x4 st. 8x1+6x2≥24 st. x1+2x2+3x3=15 4x1+6x2≥-12 2x1+ x2+5x3=20 2x2≥4 x1+2x2+ x3+ x4=10 x1, x2≥0

>>闁诲繒鍋炲ú鏍閹达箑绀傞柕濠忛檮閻庯拷<<
12@gma联系客服:779662525#qq.com(#替换为@)