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. : u, T+ u3 N- |) ], k2 S" t 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? $ I& S: G) Q( \: b( P7 y: t. j; }) @ If an extreme point is optimal, then is it possible that not all z_j-c_j≥0 for an associated basis?2 V" P/ G, S5 |) C0 G3 d3 K0 c
If there exists a d such that Ad=0,d≥0, and cd≥0, then is the optimal objective value unbounded? 4 c, ]! I! v+ q6 p Let x ̅ be a feasible solution with exactly m positive components. Is x ̅ necessarily an extreme point of X? : ]0 o6 G. p6 ? If a nonbasic variable x_k has z_k-c_k=0 at optimality, then can one claim that alternative optimal solutions exist? . B5 H8 y8 ~7 A" h. p" ^& P 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.4 }3 ]1 [5 E+ x3 U+ l
Is it possible for an optimal solution to have more than m positive variables?- [9 Z$ P( `! P$ A, O: }3 R* Y
Suppose that n=m+1. What is the least upper bound on the number of extreme points and feasible bases?8 @4 u$ j& O3 T% k" T# ^6 \
A p-dimensional polyhedron can have at most p extreme directions. True or false? Explain.4 [9 D! ]* P! U* e: 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. 5 {+ J9 U( C1 N9 }: R " k- R/ q# q' i作者: z919953051 时间: 2014-11-8 13:52
你这个可以用于ACM竞赛了。。。 9 |( s) _/ P( L' w( S" A作者: wangxiaohan 时间: 2015-1-18 06:15
好高深呀帮顶下 7 o' V1 O0 m8 P" D5 W& `作者: 士心之约 时间: 2015-10-2 09:00 ( V" h, U" M7 }
帮顶下