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Graphical solution of the prototype example: a 2-var LP with a unique optimal solution

The `` sliding motion'' described above suggests a way for identifying the optimal values for, let's say, a max LP problem. The underlying idea is to keep ``sliding'' the isoprofit line tex2html_wrap_inline1629 in the direction of increasing tex2html_wrap_inline1611 's, until we cross the boundary of the LP feasible region. The implementation of this idea on the prototype LP of Equation 5 is depicted in Figure 3.

Figure 3: Graphical solution of the prototype example LP

From this figure, it follows that the optimal daily production levels for the protoype LP are given by the coordinates of the point corresponding to the intersection of line tex2html_wrap_inline1633 with the tex2html_wrap_inline1461 -axis, i.e., tex2html_wrap_inline1637 . The maximal daily profit is tex2html_wrap_inline1639 . Notice that the optimal point is one of the ``corner'' points of the feasible region depicted in Figure 3. Can you argue that for the geometry of the feasible region for 2-var LP's described above, if there is a bounded optimal solution, then there will be one which corresponds to one of the corner points? (This argument is developed for the broader context of n-var LP's in the next section.)

UAL Data
Fri Jun 20 15:03:05 CDT 1997