The most typical way to represent a two-variable function
is to perceive it as a surface in an (orthogonal) three-dimensional
space, where two of the dimensions correspond to the independent
variables and , while the third dimension provides the
function value for any pair . However, in the context of
our discussion, we are interested in expressing the information
contained in the two-var LP objective function in the
Cartesian plane defined by the two independent variables and
. For this purpose, we shall use the concept of *contour
plots*. Contour plots depict a function by identifying the set of
points that correspond to a constant value of the function
, for any given range of 's. The plot
obtained for any fixed value of is a contour of the
function. Studying the structure of a contour is expected to identify
some patterns that essentially depict some useful properties of the
function.

In the case of LP's, the linearity of the objective function implies that any contour of it will be of the type:

i.e., a straight line. For a maximization (minimization) problem, this
line will be called an *isoprofit (isocost)* line. Assuming that
(o.w., work with ), Equation 12 can be
rewritten as:

which implies that by changing the value of , the resulting isoprofit/isocost lines have constant slope and varying intercept, i.e, they are parallel to each other (which makes sense, since by the definition of this cocnept, isoprofit/isocost lines cannot intersect). Hence, if we continously increase from some initial value , the corresponding isoprofit lines can be obtained by ``sliding'' the isprofit line corresponding to parallel to itself, in the direction of increasing or decreasing intercepts, depending on whether is positive or negative.

Fri Jun 20 15:03:05 CDT 1997