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To solve the given Linear Programming Problem (LPP) using the Dual Simplex Method, we first need to convert the problem into its standard form. The problem is: Minimize: \[ z = 3x_1 + x_2 \] Subject to the constraints: \[ 2x_1 + x_2 \geq 4 \] \[ x_1 + 2x_2 \geq 6 \] \[ x_1, x_2 \geq 0 \] ### Step 1: Convert to Standard Form The standard form requires all constraints to be equalities with non-negative right-hand sides. We introduce surplus variables \( s_1 \) and \( s_2 \) to convert the inequalities: \[ 2x_1 + x_2 - s_1 = 4 \] \[ x_1 + 2x_2 - s_2 = 6 \] \[ x_1, x_2, s_1, s_2 \geq 0 \] ### Step 2: Initial Tableau The initial tableau for the Dual Simplex Method is constructed as follows: \[ \begin{array}{cccccc|c} & x_1 & x_2 & s_1 & s_2 & \text{RHS} \\ \hline z & -3 & -1 & 0 & 0 & 0 \\ \hline s_1 & -2 & -1 & 1 & 0 & -4 \\ s_2 & -1 & -2 & 0 & 1 & -6 \\ \end{array} \] ### Step 3: Identify the Pivot _________ _____ ______ ________ ____ ________ ________ ___.
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