In this section, we develop a solution approach for LP problems,
which is based on a geometrical representation of the feasible region
and the objective function. In particular, the space to be considered
is the *n*-dimensional space with each dimension defined by one
of the LP variables . The objective
function will be described in this *n*-dim space by its
*contour plots*, i.e., the sets of points that correspond to
the same objective value. To the extent that the proposed approach
requires the visualization of the underlying geometry, it is
applicable only for LP's with upto three variables. Actually, to
facilitate the visualization of the concepts involved, in this
section we shall restrict ourselves to the two-dimensional case,
i.e., to LP's with two decision variables. In the next section, we
shall generalize the geometry introduced here for the 2-var case, to
the case of LP's with *n* decision variables, providing more
analytic (algebraic) characterizations of these concepts and
properties.

- Feasible Regions of Two-Var LP's
- The solution space of a single equality constraint
- The solution space of a single inequality constraint
- Representing the Objective Function in the LP solution space
- Graphical solution of the prototype example: a 2-var LP with a unique optimal solution
- 2-var LP's with many optimal solutions
- Infeasible 2-var LP's
- Unbounded 2-var LP's

Fri Jun 20 15:03:05 CDT 1997