Problem $3$:

Consider the following IP problem:

Maxz$=8x_1+5x_2$

Subject $to$

$,x_1+x_{2}6$

$,9x_1+5x_{2}45$

$,x_1,x_{2}0$; and integers

The following figure shows the branch and bound tree for the IP problem, where $t$ is the order of solving the subproblems:

Answer the following:

a$)$ For each subproblem identify the reason for branching or fathoming the subproblem.

b$)$ Write the complete LP model for subproblem $5.$

c$)$ What is the optimal solution for the IP problem?