Maximize z $=10$x$1+12$x$2+7$x$3+3/2$x$4$

Subject to$,$

$4$x$1+5$x$2+3$x$3+1$x$4<=10$

Use the LP$-$based branch$-$and$-$bound algorithm discussed in class to solve this problem by

hand. For each subproblem, solve its LP relaxation using GAMS and its default solver.