Indicate which of the following is an all$-$integer linear program and which is a mixed$-$integer linear program. Write the LP Relaxation for the problem but do not attempt to solve.

$($a$)$

Max $40$x$1+35$x$2$

s$.$t$.$

$(1)9$x$1+4\mathrm{.}5$x$2<=400$

$(2)4\mathrm{.}5$x$1+2$x$2<=250$

$(3)$ x$1+$ x$2<=150$

x$1,$ x$2>=0$ and x$2$ integer