Consider the following IP problem. Max z = 5x1+x2
s. t. − x1 + 2x2 ≤ 4
x1 − x2 ≤ 1
4x1 + x2 ≤ 12
x1,x2 ∈Z+
1. Solve graphically
2. Solve the LP relaxation of the problem graphically. Round this solution to the nearest integer solution and check whether it is feasible. Then enumerate all the rounded solutions by rounding this solution for the LP relaxation in all possible ways (i. e., by rounding each non-integer value both up and down). For each rounded solution, check for feasibility and, if feasible, calculate z. Are any of these feasible rounded solutions optimal for the IP problem?