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.
- f: W6 U1 t6 ^        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?
. h7 H& y7 m3 J4 `        If an extreme point is optimal, then is it possible that not all z_j-c_j≥0 for an associated basis?
* g; O0 a3 ?/ G. \9 ^- F! }        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?
        If a nonbasic variable x_k has z_k-c_k=0 at optimality, then can one claim that alternative optimal solutions exist?
# t, e6 h+ E' h. i7 s6 `' u        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.
8 }; l! D6 I$ ~; ]- ?. |& D# B4 H; ?        Is it possible for an optimal solution to have more than m positive variables?
' \$ d; ]2 @4 N. f        Suppose that n=m+1. What is the least upper bound on the number of extreme points and feasible bases?
$ s+ J1 L# V5 e$ P6 L! f; a3 \: J        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.
8 A5 A& _' O0 j. E& V( O; X

z919953051

你这个可以用于ACM竞赛了。。。

wangxiaohan

好高深呀帮顶下

士心之约