Linear Programming Samples

Finite Optimal Solution Sample

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

The feasible region is bounded and nonempty. Thus if the ploblem has optimal solution, it will be finite

In addition the objective function grows in the direction of growth of x and y coordinates, the problem is as finite optimal solution will also be achieved which one of the endpoints of the feasible region
Clearily, even at simple view is visible that the maximum is reached at point (3 / 2, 1 / 2) with optimal value for objective function 3.

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