The owner of the Consolidated Machine Shop has $10,000 available to purchase a lathe, a press, a grinder, or some combination thereof. The following 0-1 integer linear programming model has been developed to determine which of the three machines (lathe, x₁; press, x2; or grinder, x3) should be purchased in order to maximize annual profit:
maximize Z 1,000x₁ +700x₂+ 800x₃ (profit, S)
$5,000x₁+ 6,000x₂ +4,000x₃ ≤ 10,000 (cost, S)?
What would be the constraint that either lathe or press (not both) should be purchased?
1) x₁-x₂ ≤0
2) x₁+x₂ ≤1
3) x₁-x₂≤ 1
4) x₁-x₂=0