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We are asked to solve the LPP using the dual simplex method. Let’s solve it step by step manually. We have: Minimize: [ z = 3x_1 + x_2 ] Subject to: [ x_1 + x_2 \ge 1 ] [ 2x_1 + 3x_2 \ge 2 ] [ x_1, x_2 \ge 0 ] --- Step 1: Convert constraints to standard form for dual simplex For the dual simplex method, all constraints should be of the form (\le) for a minimization problem, but it’s more common to convert (\ge) constraints into (\le) by introducing surplus variables: [ x_1 + x_2 - s_1 = 1, \quad s_1 \ge 0 ] [ 2x_1 + 3x_2 - s_2 = 2, \quad s_2 \ge 0 ] Now the system becomes: [ x_1 + x_2 - s_1 = 1 ] [ 2x_1 __________ __________ __________ _____ ______ __________ ________ ______ __________ ___ _________ _____.
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