Problem $11-1($a$)$ Indicate whether the following linear program is an all$-$integer linear program or a mixed$-$integer linear program. Max $30$x$1+25$x$2$ s$.$t$.3$x$1+1\mathrm{.}5$x$2<=4001\mathrm{.}5$x$1+2$x$2<=2501$x$1+1$x$2<=150$ x$1,$ x$2>=0$ and x$2$ integer This is a mixed$-$integer linear program. Write the LP Relaxation for the problem but do not attempt to solve. If required, round your answers to one decimal place. Its LP Relaxation is Max x$1+$ x$2$ s$.$t$.$ x$1+1\mathrm{.}5$x$2<=1\mathrm{.}5$x$1+$ x$2>$ x$1+$ x$2<=$ x$1,$ x$2<=0$ and x$1$ integer $($b$)$ Indicate whether the following linear program is an all$-$integer linear program or a mixed$-$integer linear program. Max $3$x$1+4$x$2$ s$.$t$.2$x$1+4$x$2>=8>2$x$1+6$x$2>=12$ x$1,$ x$2>=0$ and integer This is a mixed$-$integer linear program. Write the LP Relaxation for the problem but do not attempt to solve. If required, round your answers to one decimal place. Its LP Relaxation is Max x$1+$ x$2$ s$.$t$.2$x$1+$ x$2>$ x$1+6$x$2<=$ x$1,$ x$2>0$ and x$1$ integer