【摘要】 本文报导了线性规划最优对偶解的如下一个性质,即以最优对偶解按本文所述方式变换原问题的系数,并组成新的线性规划问题时,新的最优对偶解值全为1。本文对此现象作了经济意义上的解释。更多还原

【Abstract】 An interesting property of the optimal dual solution of LP,that was notmentioned in textbooks or research reports in the past,may be described asfollowing:Suppose a LP problem is expressed asmax C·Xs.t.A·X≤B（1）x≥0where,C=（c₁,c₂,…,c_n）,X=（x₁,x₂,…,x_n）^r,B=（b₁,b₂,…,b_n）^T,and A=（a_i）_m×nLet D=（d₁,d₂,…,d_n）^T be the optimal dual solution,and all components ofwhich are assumed to be nonzero.Then if the components of matrices C,B andA in（1）are replaced by:c’_i=c_i·1/d_i,b’i=b_j·1/d_j,a’_ij=a_ij·d_i/d,（2）the components of the new optimal dual solution would all be unity,i.e.D′=（1,1,1…,1）^T.This property would be useful in explaining the economic meaningof the optimal dual solution of LP in some special cases.更多还原