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

Max 30x₁+ 25x₂

s.t.

3x₁+ 1.5x₂ 400

1.5x₁+ 2x₂ 250

1x₁+ 1x₂ 150

x₁,x₂ 0 andx₂integer

Write the LP Relaxation for the problem but do not attempt to solve.

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

Max 3x₁+ 4x₂

s.t.

2x₁+ 4x₂ 8>

2x₁+ 6x₂ 12

x₁,x₂ 0 and integer

Write the LP Relaxation for the problem but do not attempt to solve.