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justification for it.

(a)  For any given LP, if xis a feasible solution that is not optimal, then there exists an improving, feasible direction at x.

(b)  For a given LP in standard form and a given basis matrix B, if both the primal and dual solutions corresponding to B are feasible, then they are both optimal.

(c)  For a given LP in standard form and a given basis matrix B, if the dual solution corresponding to B is infeasible, then the primal solution cannot be optimal.

(d)      For any given LP, if there exists an optimal solution, there exists an optimal solution that is basic feasible.

(e)      A self-dual LP (a problem whose dual is itself) can be unbounded.

(f)  For an LP in standard form, no more than m variables can be positive at any optimal solution, where m is the number of equality constraints.

(g)     An iteration of the simplex method may move the feasible solution by a positive distance while leaving the cost unchanged.

(h)    We can detect whether an LP is unbounded at the end of Phase I, while applying two-phase method.

(i) We can detect whether an LP is infeasible at the end of Phase I, while applying two-phase method.

(j) While running the simplex method, the reason that minimum ratios are used to determine the departing variable is to reach the optimal solution as fast as possible.

al-
True
Yes it in Bomible
Consider
max
4 X !
-+ 5k2
Sub
241 + X2 &lt; 8
With H = 1 X2 = 3
So
we try to Complementry slack nese
theorem
and find
n = (1:3) which is
yearible To
how of optimal -
4 ,...

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