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What does Phase I of the simplex method do when no starting extreme point is known?
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optimization
Constraint set bounded by the five lines x1 = 0, x2 = 0, x1 = 8, x2 = 5, and x1 + x2 = 10. These enclose an infinite number of points that represent feasible solutions.
In the simplex method, which is a standard linear programming algorithm, the procedure typically assumes that an initial extreme point (or vertex) is already known.
When no starting extreme point is available, a variant of the algorithm known as Phase I is employed. The primary purpose of Phase I is to either find a valid starting extreme point or to determine that the problem has no feasible solutions. Once a feasible extreme point is identified, the standard simplex method can proceed to test for optimality and navigate toward the optimal solution.12