Obviously if the model wants to upgrade the kitchen, it should be done by either the landlord or a subcontractor. As he creates the IP model, the landlord wants to leave the choice of whether to actually upgrade the kitchen up to the optimization algorithm. How should this constraint be written if he uses the following scheme for decision variables? 5 points
x1 = contractor works on wood floors x2 = landlord works on wood floorsx3 = contractor works on kitchen tile x4 = landlord on kitchen tilex5 = contractor works on back door x6 = landlord works on back doorx7 = contractor works on garage door x8 = landlord works on garage doorA) x3 + x4 ≤ 1B) x3 + x4 = 1C) x3 - x4 ≤ 1D) x3 - x4 = 1

We need a multiple choice constraint. Constraint x3+x4 <= 1 states that only one of the 2 options of landlord or contractor working on kitchen tiles can be used. (Assuming x3, x4 are binary variables)

Hence if x3 = 1, x4 is 0, and if x4=1, x3 becomes 0. Please note, there is no constraint in question specifying that kitchen tile has to be done. Hence, both x3 and x4 can be 0 depending on cost optimization, and x3+x4<=1 will still hold correct.