Primal Simplex

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Canonical Form:

Z function values move to the LHS. e.g. z=2x1+3x2 -> z-2x1-3x2=0

All constraints with <= get +Si. e.g. x1+x2<=5 -> x1+x2+S1=5

Solving:

Pick entry column (Min Problem -> highest positive; Max Problem -> largest negative)

Calculate Ratios (RHS / value in entry column)

Pick entry row (Lowest positive ratio)

Pivot

When no entry columns available; table is optimal.

Special Cases:

Case 1: Unique Solution

Case 2: Multi-solution (Non-basic decision variables; Objective function RHS = 0)

Case 3: Infeasible

Case 4: Unbound (All ratios are negative)