标题: 求助，单纯形法习题 [打印本页] 作者: lianfs 时间: 2014-11-5 20:50 标题: 求助，单纯形法习题 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. % j/ D/ w& R( x$ G2 [ 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? , s$ y" |: }8 I/ B" ?7 @ If an extreme point is optimal, then is it possible that not all z_j-c_j≥0 for an associated basis?( n# J! s/ C4 X% Y4 X$ @, P
If there exists a d such that Ad=0,d≥0, and cd≥0, then is the optimal objective value unbounded?. J, m+ p M8 ?9 k( |1 A8 H N \
Let x ̅ be a feasible solution with exactly m positive components. Is x ̅ necessarily an extreme point of X? " r/ X6 J* j" U+ `$ X2 W If a nonbasic variable x_k has z_k-c_k=0 at optimality, then can one claim that alternative optimal solutions exist?" E! V( L) x( h/ a
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./ |+ Q, N4 m& Z6 S# y3 c* P
Is it possible for an optimal solution to have more than m positive variables? / M6 \9 z0 e O6 S4 S. Y Suppose that n=m+1. What is the least upper bound on the number of extreme points and feasible bases? # p8 X8 }! z* k* B3 t A p-dimensional polyhedron can have at most p extreme directions. True or false? Explain.7 e- X% ?( b/ b. I% |8 I
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.2 n% w' C; H( P; B* I
/ ^: R6 x7 E9 B8 p9 R& ` 作者: z919953051 时间: 2014-11-8 13:52
你这个可以用于ACM竞赛了。。。( ~* v: ? G$ n: ]) `' J4 C7 l t 作者: wangxiaohan 时间: 2015-1-18 06:15
好高深呀帮顶下' v ]9 q+ \# N7 u 作者: 士心之约 时间: 2015-10-2 09:00 3 W; N# x' i. Q: s5 `
帮顶下' v ]9 q+ \# N7 u
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