Consider an integer program $($IP$)$: max x$1,$x$2,$x$3$ in S x$1+2$x$2+3$x$3(4)$ where S is a integer linear set. This IP can be solved by using the branch$-$and$-$bound algorithm. When you solve the initial LP relaxation, its solution is fractional, so you split the problem in two and solve each of the new LPs$.$ The first problem yields a solution $(2,0,1).1.(15$pt$)$ If the second problem yields a solution $(0,0\mathrm{.}5,0\mathrm{.}5).$ What would you do next? $2.(10$pt$)$ If the second problem yields a solution $(0,2\mathrm{.}5,0\mathrm{.}5).$ What would you do next?