Problem $11-1$

$($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 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

Sax $x_1+x_2$

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

$x_1,x_2{x}_1+,x_2.$

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

Max$3x_1+4x_2$

s$.$t$.$

$2x_1+4x_{2}8>$

$2x_1+6x_{2}12$

$x_1,x_{2}0$ and integer

This is a 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