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 $50$x$1+45$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

Is this linear program an all$-$integer linear program or a mixed$-$integer linear program?

This is an all$-$integer linear program.

This is a mixed$-$integer linear program.

Write the LP Relaxation for the problem.

Max

s$.$t$.$

$(1)$

$(2)$

$(3)$

$---$Select$---$

$($b$)$

Min $5$x$1+6$x$2$

s$.$t$.$

$(1)4$x$1+6$x$2>=8$

$(2)4$x$1+8$x$2>=12$

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

Is this linear program an all$-$integer linear program or a mixed$-$integer linear program?

This is an all$-$integer linear program.

This is a mixed$-$integer linear program.

Write the LP Relaxation for the problem.

Min

s$.$t$.$

$(1)$

$(2)$

$---$Select$---$