Question

Problem 11-1

(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 and x2 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	x1 + x2
s.t.
	x1 + 1.5x2 ≤
	1.5x1 + x2 >
	x1 + x2 ≤
	x1 , x2 ≤  0 and x1 integer

(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

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	x1 + x2
s.t.
	2x1 + x2 >
	x1 + 6x2 ≤
	x1 , x2 >  0 and x1 integer

Answer 1