While implementing the Branch & Bound algorithm, use Pyomo to solve the LP relaxation subproblems at each node $($all variable domains set to $$NonNegativeReals$).$

Use the MIP branch$-$and$-$bound algorithm to solve the following MIP problem interactively:

Maximize

Z $=5$ x$1+4$ x$2+4$ x$3+2$ x$4,$

subject to

X$1+3$ x$2+2$ x$3+$X$4<=10$

$5$ x$1+$ x$2+3$ x$3+2$ x$4<=15$

X $1+$ x$2+\backslash$times $3+$ x$4<=6$

and xj $>=0,$ for j $=1,2,3,4$

xj is integer, for j $=1,2,3$