مشاهده نسخه کامل
: f_1367
14-04-2013, 16:53
سلام
یه سوال چند قسمتی از بهینه سازی خطی دارم سوالش به زبان اصلیه ممنون میشم اگه کسی حلش کنه
Consider the standard form polyhedron P = {x I Ax = b, x :::::
O } . Suppose that the matrix A has dimensions m x n and that its rows are
linearly independent . For each one of the following statements, state whether it
is true or false. If true, provide a proof, else, provide a counterexample.
(a) If n = m + 1 , then P has at most two basic feasible solutions .
(b) The set of all optimal solutions is bounded.
(e) At every optimal solution, no more than m variables can be positive.
(d) If there is more than one optimal solution, then there are uncountably
many optimal solutions.
(e) If there are several optimal solutions , then there exist at least two basic
feasible solutions that are optimal.
(f) Consider the problem of minimizing max{ e'x, d'x} over the set P. If this
problem has an optimal solution, it must have an optimal solution which
is an extreme point of P.
یه سوال چند قسمتی از بهینه سازی خطی دارم سوالش به زبان اصلیه ممنون میشم اگه کسی حلش کنه
Consider the standard form polyhedron P = {x I Ax = b, x :::::
O } . Suppose that the matrix A has dimensions m x n and that its rows are
linearly independent . For each one of the following statements, state whether it
is true or false. If true, provide a proof, else, provide a counterexample.
(a) If n = m + 1 , then P has at most two basic feasible solutions .
(b) The set of all optimal solutions is bounded.
(e) At every optimal solution, no more than m variables can be positive.
(d) If there is more than one optimal solution, then there are uncountably
many optimal solutions.
(e) If there are several optimal solutions , then there exist at least two basic
feasible solutions that are optimal.
(f) Consider the problem of minimizing max{ e'x, d'x} over the set P. If this
problem has an optimal solution, it must have an optimal solution which
is an extreme point of P.