求助，单纯形法习题

lianfs

Answer the following questions along with a concise explanation with respect to the linear program to maximize cx subject to x∈X={x:Ax=b,x≥0}, where A is m×n of rank m<n.
7 i0 }' `6 C3 _, v        In a simplex tableau, if z_j-c_j=-7 for a nonbasic variable x_j, what is the change in objective value when x_j enters the basis given that the minimum ratio is 3 in the pivot?
        If an extreme point is optimal, then is it possible that not all z_j-c_j≥0 for an associated basis?
        If there exists a d such that Ad=0,d≥0, and cd≥0, then is the optimal objective value unbounded?
        Let x ̅ be a feasible solution with exactly m positive components. Is x ̅ necessarily an extreme point of X?
9 U  C; T: C. ~* B, k: \        If a nonbasic variable x_k has z_k-c_k=0 at optimality, then can one claim that alternative optimal solutions exist?
        If x_1 and x_(2 )are adjacent points and if B_1 and B_2 are respective associated bases, then these bases are also adjacent. True or false? Explain.
  `" M3 t! e1 H( j        Is it possible for an optimal solution to have more than m positive variables?
        Suppose that n=m+1. What is the least upper bound on the number of extreme points and feasible bases?
! B' h' l' e9 E% x2 q        A p-dimensional polyhedron can have at most p extreme directions. True or false? Explain.
; f  j% ]# s# g1 S7 _        Let x ̅ be an extreme point having (m-1) positive components. Then there are (p+1) bases associated with this extreme point, where p=n-m. True or false? (Assume that Ax=b does not imply any variable to be a constant) Explain.

* p" Y' L' [+ s$ x$ H& ^% J

z919953051

你这个可以用于ACM竞赛了。。。

wangxiaohan

好高深呀帮顶下
) U) L; s, ~% u: Q8 d# H2 K9 L

士心之约