Answer Happy

Solve the following problem by the Dantzig-Wolfe decomposition technique using two convexity constraints: maximize z = subject to X1 + X2 +3X3 -X4, 2x₁ + x₂ + x3 + x4 ≤12, ≤ 2, ≤ 5, X3+x4≤ 4, -X3 + x4≤ 5, X1, X2, X3, X4 ≥ 0. - X1 + X2 3x1 - 4x3 Keep constraints 1 and 3 in the master problem. Note that the first sub-problem (with respect to x₁ and x2) has an unbounded feasible region. In this case, you may generate an extreme direction instead of an extreme point at certain iterations. In class we only discussed the case of bounded sub-problems. You need to read Section 7.4 from the textbook to learn how to handle extreme directions. Otherwise, add the constraint (upper bound) x₁ ≤ 10 to the problem. This constraint will not affect the optimal solution.