Consider the following branch$-$and$-$bound tree for solving a three$-$variable pure

integer programming problem.$$

Is it a minimization or maximization problem? Why?

$(2)$ What is the best $($and correct$)$ upper bound to the IP that can be deduced?

$(3)$ What is the best $($and correct$)$ lower bound to the IP that can be deduced?

$(4)$ Write down the additional constraints of the linear programming relaxation solved at

node $8$ compared to that solved at the root.

$(5)$ Which nodes are candidates to explore next if node $4$ has a fractional solution with

z$=17\mathrm{.}5?$

$(6)$ Which LP was solved first: The one corresponding to Node $5$ or the one corresponding

to Node $6?$ Why?

$2$