Show me Step by step answer for the below problems:

1. Consider the following linear program. min:2x1+4x2s.t.x1+x282x1+3x26x1x22x1+2x23x1,x20 i. Use the graphical method to identify the feasible region and optimal solution to the linear program. ii. Consider the integer program with objective (1), constraints (2) to (5), and (6) replaced with x1,x2{0Z+}. Use the graphical method to identify the feasible region and optimal solution to the integer program. iii. Devise an objective function that would cause the linear program to have multiple optimal solutions. iv. For this set of constraints, can you devise an objective function that would result in multiple optimal integer solutions? Why or why not? If you can, provide one example. v. Devise new constraints that would cause the linear program to be feasible but the integer program to be infeasible