Explain the step by step procedure of revised simplex method.
Answers
For the rest of the discussion, it is assumed that a linear programming problem has been converted into the following standard form:
{\displaystyle {\begin{array}{rl}{\text{minimize}}&{\boldsymbol {c}}^{\mathrm {T} }{\boldsymbol {x}}\\{\text{subject to}}&{\boldsymbol {Ax}}={\boldsymbol {b}},{\boldsymbol {x}}\geq {\boldsymbol {0}}\end{array}}}
\begin{array}{rl}
\text{minimize} & \boldsymbol{c}^{\mathrm{T}} \boldsymbol{x} \\
\text{subject to} & \boldsymbol{Ax} = \boldsymbol{b}, \boldsymbol{x} \ge \boldsymbol{0}
\end{array}
where A ∈ Rm×n. Without loss of generality, it is assumed that the constraint matrix A has full row rank and that the problem is feasible, i.e., there is at least one x ≥ 0 such that Ax = b. If A is rank-deficient, either there are redundant constraints, or the problem is infeasible. Both situations can be handled by a presolve step.
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