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?
0 |# f6 _2 [( S( T8 `        If an extreme point is optimal, then is it possible that not all z_j-c_j≥0 for an associated basis?
7 u7 `$ p; o" D4 S1 l- D        If there exists a d such that Ad=0,d≥0, and cd≥0, then is the optimal objective value unbounded?
, H) i, A+ Q& C1 C        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?
; D1 j4 Q% I9 T; }        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.
) ~( K4 D7 g# p0 V  b8 p        Is it possible for an optimal solution to have more than m positive variables?
: A& g4 ?% \  z% W        Suppose that n=m+1. What is the least upper bound on the number of extreme points and feasible bases?
$ M8 V/ V- D+ {  \$ |5 f        A p-dimensional polyhedron can have at most p extreme directions. True or false? Explain.
        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.

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z919953051

你这个可以用于ACM竞赛了。。。

wangxiaohan

好高深呀帮顶下
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士心之约