Question

A landlord is considering upgrades and repairs, including wood floors, kitchen tile, a new back door, and a repaired garage door. The landlord could do these things himself or hire a contractor. The contractor could finish the job in half the time but would charge more. The landlord wants to leave the choice of whether to actually upgrade the kitchen tile up to the optimization algorithm. How should this constraint be written if he uses the following scheme for decision variables? x1 = contractor works on wood floors x2 = landlord works on wood floors x3 = contractor works on kitchen tile x4 = landlord works on kitchen tile x5 = contractor works on back door x6 = landlord works on back door x7 = contractor works on garage door x8 = landlord works on garage door Group of answer choices x3+ x4≤ 1 x3+ x4= 1 x3- x4= 1 x3- x4≤ 1

Answer 1

x3 + x4 ≤ 1

Explanation:

Upgrades considered = wood floors, Kitchen tile, New back door and a repaired garage

The constraint of whether to upgrade the kitchen either by the landlord or by a contractor can be represented with the scheme below:

x3 + x4 ≤ 1

The constraint is written this way because only one scheme can be used at a time i.e when x3 = 1 , x4 = 0 and vice versa. also

note that both x3 and x4 can be = 0. because the upgrade of the kitchen tiles is under probability and the landlord might decide not to upgrade the kitchen tiles hence both schemes ( x3 and x4 ) can be = 0