4.4 . The following questions below apply to the linear program minimize z = ?? 101...

$\mathrm{4.4}.$ The following questions below apply to the linear program$$minimize z $=\mathrm{â??}\mathrm{101}$x$1+\mathrm{87}$x$2+\mathrm{23}$x$3$subject to $6$x$1\mathrm{â??}\mathrm{13}$x$2\mathrm{â??}3$x$3<=\mathrm{11}6$x$1+\mathrm{11}$x$2+2$x$3<=\mathrm{45}$x$1+5$x$2+$ x$3<=\mathrm{12}$x$1,$ x$2,$ x$3>=0$with optimal basic solution$$basic x$1$ x$2$ x$3$ x$3$ x$4$ x$5$ rhs$\mathrm{â??}$z $000\mathrm{12}45\mathrm{372}$x$11001\mathrm{â??}275$x$2010\mathrm{â??}49\mathrm{â??}\mathrm{30}1$x$3001\mathrm{19}\mathrm{â??}\mathrm{43}\mathrm{144}2$All of the questions are independent.$($i$)$ What is the solution of the linear program obtained by decreasing the right$-$hand$$side of the second constraint by $\mathrm{15}?($ii$)$ By how much can the right$-$hand side of the second constraint increase and$$decrease without changing the optimal basis?