Parametric Linear Programming

In the general linear-programming problem of

$$ \begin{array}{ll} & \quad {\rm Minimize}\quad \boldsymbol{c}^{T}{x} \\ & {\rm subject}\,{\rm to}\quad \boldsymbol{A x}=\boldsymbol {b} \\ & \qquad \qquad \qquad {\boldsymbol{x}\geq 0}\end{array} $$

it is often appropriate to study how the optimal solution changes when some of the data are functions of a single parameter $\uplambda$. Most mathematical programming systems allow parametric analysis of the cost coefficients (PAROBJ), the right-hand-side elements (PARARHS), joint analysis of the objective function and right-hand-side elements (PARARIM), and the parametric analysis of the data in a row (PARAROW).