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.
        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?
) E& X6 G# @+ |+ l4 y$ s  U! k) K        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?
) g- e8 O/ `: q        Let x ̅ be a feasible solution with exactly m positive components. Is x ̅ necessarily an extreme point of X?
        If a nonbasic variable x_k has z_k-c_k=0 at optimality, then can one claim that alternative optimal solutions exist?
6 j) W, K; R" R2 A6 M& i( R& i        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.
        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?
5 g* U, b0 F! s. L: I5 j* V( B        A p-dimensional polyhedron can have at most p extreme directions. True or false? Explain.
& |, ~( o6 U+ }% m4 q! l        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.

z919953051

你这个可以用于ACM竞赛了。。。
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wangxiaohan

好高深呀帮顶下
1 k2 K$ I3 B; Y7 R8 g/ p1 v: {

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