The plot below depicts the solution space of pure binarary ILP min 3x1 + 4x2 s.t. 4x1
Question:
The plot below depicts the solution space of pure binarary ILP min 3x1 + 4x2 s.t. 4x1 + 2x2 Ú 1 5x1 + 10x2 Ú 4 x1, x2 = 0 or 1
Coordinates and solution values of important points are pre-computed in the key.
(a) Sketch the convex hull of integer solutions on the plot and briefly justify your choice.
(b) Determine the dimension of the convex hull, and justify your answer with suitable affinely independent points.
(c) Determine graphically whether each of the three inequalities below is valid. Then, determine whether each intersects the convex hull in a facet, or in a face of lower dimension, or not at all, including calling out affinely independent points that satisfy the cuts as equalities in the facet and face cases.
4x1 + 2x2 Ú 1 5x1 + 2x2 Ú 2 x1 + x2 Ú 1
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