$($a$)$ Indicate whether the following linear program is an all$-$integer linear program or a mixed$-$integer linear program.

Max$30x_1+25x_2$

s$.$t$.$

$3x_1+1\mathrm{.}5x_{2}400$

$1\mathrm{.}5x_1+2x_{2}250$

$1x_1+1x_{2}150$

$x_1,x_{2}0$ 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

$x_1+$

$x_2$

$s.t.$

$x_1+1\mathrm{.}5x_2.$

$1\mathrm{.}5x_1+x_2$

$x_1+$

$x_2-=$

$x_1,x_2$