We apply a branch and bound methodology to solve a MAXIMIZATION integer program with two binary decision variables denoted as x₁ and x₂. For each scenario, indicate whether we should branch or if we can fathom and why we can fathom. (Solve each part independently). (2 points each)

1. The incumbent solution is 150. The LP relaxation objective function value is 100 with x₁ = 0.4 and x₂ = 0.7.

2. The incumbent solution is 100. The LP relaxation objective function value is 104 with x₁ = 0 and x₂ = 1.

3. The incumbent solution is 75. The LP relaxation objective function value is 100 with x₁ = 0.7 and x₂ = 1.

4. The incumbent solution is 150. The LP relaxation is infeasible.