Consider a pure-integer program over constraints

-1x1 + 2x2 … 4 5x1 + 1x2 … 20

-2x1 - 2x2 … -7 x1, x2 Ú 0 and integer

(a) Draw a 2-dimensional plot of the LPrelaxation feasible set.

(b) Identify all integer-feasible solutions and their convex hull.

(c) Determine the dimension of this convex hull.

(d) Identify all facet-defining inequalities of the convex hull and the required affinely independent solutions proving each.

(e) Identify another non-facet-defining inequality that at least intersects the convex hull.

(f) Identify another valid inequality that cuts off part of the LP-feasible set without intersecting the convex hull at all.