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Definition: Optimal Feasible Solution
Any vector $\b{x} $ that yields the minimum value of the objective function $\transpose{ \b{c}}\b{x} $ over the set of vectors satisfying the constraints $\b{Ax = b, x \geq 0} $ is said to be an optimal feasible solution.
Theorem
: Fundamental Theorem of LP
Consider a linear program in standard form.
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If there exists a feasible solution, then there exists a basic feasible solution.
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If there exists an optimal feasible solution, then there exists an optimal basic feasible solution.