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.
9 [. \/ _, G  u$ {* e        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?
- _  T5 \0 F) X        If an extreme point is optimal, then is it possible that not all z_j-c_j≥0 for an associated basis?
- G5 c+ y$ l7 a        If there exists a d such that Ad=0,d≥0, and cd≥0, then is the optimal objective value unbounded?
* Z: }0 A# o' ~1 u        Let x ̅ be a feasible solution with exactly m positive components. Is x ̅ necessarily an extreme point of X?
2 Z" u* w* r+ \6 Z/ T  U        If a nonbasic variable x_k has z_k-c_k=0 at optimality, then can one claim that alternative optimal solutions exist?
9 p! h: A  g+ s; k        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.
0 q. D6 u; F; B( e3 I: |3 o: R1 N1 ^& M        Is it possible for an optimal solution to have more than m positive variables?
; Z6 G6 _) w, ]7 U        Suppose that n=m+1. What is the least upper bound on the number of extreme points and feasible bases?
  j/ v$ a+ G# J2 R: ~7 B$ v        A p-dimensional polyhedron can have at most p extreme directions. True or false? Explain.
$ {; n; Z6 w+ g: g        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.
, X! G/ o, V$ {- f/ q
2 I* _: H, O4 F

士心之约

wangxiaohan

好高深呀帮顶下

z919953051

你这个可以用于ACM竞赛了。。。