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.