Linear Programming examples

Infinite solutions example

Lets consider
Maximize (x + y)
Subject to
x + y ≤ 3
x + y ≤ 2
x - y ≥ 1
x, y ≥ 0

The Feasible region

The feasible region is bounded and nonempty.
As shown in the graph, the objective function is parallel to the lines that limit the feasible region and grows in the direction of growth of x and y coordinates the maximum is reached in any one of the points of the feasible set located at the line farthest from the origin of coordinates point, thus for all these points the objective function takes the same value, therefore have an entire segment of optimal solutions, ie we are at infinite solution case.

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