FIGURE 2.2
Optimum solution of the Reddy Mikks model
An important characteristic of the optimum LP solution is that it is always associated
with a cornel" point of the solution space (where two lines intersect). This is
true even if the objective function happens to be parallel to a constraint. For example,
if the objective function is z = 6XI + 4X2, which is parallel to constraint I, we can
always say that the optimum occurs at either corner point B or comer point C. Actually
any point on the line segment BC will be an alternative optimum (see also Example
3.5-2), but the important observation here is that the line segment BC is totally
defined by the corner points Band C.
TORA Moment.
You can use TORA interactively to see that the optimum is always associated with a
corner point. From the output screen, you can clickYi~~i¥A~N~l~~¥~~B~~; to
modify the objective coefficients and re-solve the problem graphically. You may use the
following objective functions to test the proposed idea:
(a) z = 5xI + X2
(b) Z = 5Xl + 4X2
(c) Z = Xl + 3x2
(d) Z = -Xl + 2X2
(e) z = - 2xl + Xl
(f) Z = -XI - X2