2-var LP's with many optimal solutions
Consider our prototype example with the unit profit of item
being $600 instead of $200. Under this modification, the problem isoprofit lines
become:
and they are parallel to the line corresponding to the first problem
constraint:
Therefore, if we try to apply the optimizing technique of the previous
paragraph in this case, we get the situation depicted below (Figure4),
i.e., every point in the line segment CD is an optimal point, providing
the optimal objective value of $24,000.
Figure 4: An LP with many optimal solutions
It is worth-noticing that even in this case of many optimal solutions, we
have two of them corresponding to ``corner'' points of the feasible region,
namely points C and D.
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