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求助，单纯形法习题

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自我介绍: 国立清华大学学生

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发表于 2014-11-5 20:50 |只看该作者 |倒序浏览

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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?
If an extreme point is optimal, then is it possible that not all z_j-c_j≥0 for an associated basis?
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?
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.
Is it possible for an optimal solution to have more than m positive variables?
Suppose that n=m+1. What is the least upper bound on the number of extreme points and feasible bases?
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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