X, 18 2 4 St (答案无可行解) x x3 0(j=1,2,3) 12. max S=2x,+x2+x3 4x1+2x2+2x3≥4 2x1+4x2≤20 ≥0(j=1,2,3) (答案有无穷多最优解,例如X)=(4,0,0) X2)=(00,8)) 8x1+6x2≥2 4x1+6x,≥-12 S t (答案:有可行解,最优解无界) 2x,≥4 S=x1+2x,+3 x1+2x2+3x3=15 S. t x1+2x2+x3+x4=10 (答案:有唯一最优解X=(5/25/2,5/2,0) 15.用改进单纯形法求解下列线性规划问题 max s=4x +2x x1+2x2≤6 x1+x2≤9 t. 3x1-x2≤15 (答案经两次换基迭代得问题的最优解为X=(6,360 最优值为maxS=4×6+2×3=30)4 s.t.         = + − = +  + +  0( 1,2,3) 5 2 4 3 2 18 1 2 3 1 2 1 2 3 x j x x x x x x x x j (答案:无可行解) 12. max 2 1 2 3 S = x + x + x s.t.         = + +  +  + +  0( 1,2,3) 4 8 2 16 2 4 20 4 2 2 4 1 2 3 1 2 1 2 3 x j x x x x x x x x j (答案:有无穷多最优解,例如 T X (4,0,0) (1) = T X (0,0,8) (2) = ) 13. max 1 2 S = x + x s.t.          +  − +  , 0 2 4 4 6 12 8 6 24 1 2 2 1 2 1 2 x x x x x x x (答案:有可行解,最优解无界) 14. max 1 2 2 3 3 4 S = x + x + x − x s.t.         = + + + = + + = + + = 0( 1,2,3,4) 2 10 2 5 20 2 3 15 1 2 3 4 1 2 3 1 2 3 x j x x x x x x x x x x j (答案:有唯一最优解 T X (5/ 2,5/ 2,5/ 2,0) * = ) 15. 用改进单纯形法求解下列线性规划问题: max 4 1 2 2 S = x + x s.t.         −  +  − +  , 0 3 15 9 2 6 1 2 1 2 1 2 1 2 x x x x x x x x (答案;经两次换基迭代得问题的最优解为 T X (6,3,6,0,0) * = 最优值为 max S = 46+ 23 = 30 )