Consider the integer programming problem:

maximize subject to

X1 + 2X2

Subject to

-3X1+ 4X2 4 3X1 + 2x2 11 2x1 -x2 5 X1, X2 integer.

1. determine the optimal solution and objective function value of the LP relaxation and the integer programming problem(use graphical method)

2. show graphically the convex hull of the set of all solutions to the integer programming problem

3. Solve the problem by branch and bound. Clearly show work i.e. B&B tree, the order in which you analyzed the problem at each node, incumbent solutions, result of the analysis at each node