Consider the following IP problem:

Maximize Z = 1 x₁ +3 x₂,

subject to

x₁ + 2x₂ 4

x₁ x₂ 1

4x₁ + x₂ 12

and

x₁ 0, x₂ 0

x₁, x₂ are integers.

1-

Solve this problem graphically to obtain the optimal solution.

The optimal solution is Z =

2-Solve the LP relaxation 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 noninteger 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?

True or False