The following questions refer to a capital budgeting problem with six projects represented by 0-1 variables x1, x2, X3, X4, X5, and x6: (i) Write a constraint modeling a situation in which two of the projects 1, 3, 5, and 6 must be undertaken. (ii) Write a constraint modeling a situation in which, if projects 3 and 5 must be undertaken, they must be undertaken simultaneously. (iii) Write a constraint modeling a situation in which project 1 or 4 must be undertaken, but not both. (iv) Write constraints modeling a situation where project 4 cannot be undertaken unless projects 1 and 3 also are undertaken. (v) In addition to the requirement in part (iv), assume that when projects 1 and 3 are undertaken, project 4 also must be undertaken.
Question
The following questions refer to a capital budgeting problem with six projects represented by 0-1 variables x1, x2, X3, X4, X5, and x6: (i) Write a constraint modeling a situation in which two of the projects 1, 3, 5, and 6 must be undertaken. (ii) Write a constraint modeling a situation in which, if projects 3 and 5 must be undertaken, they must be undertaken simultaneously. (iii) Write a constraint modeling a situation in which project 1 or 4 must be undertaken, but not both. (iv) Write constraints modeling a situation where project 4 cannot be undertaken unless projects 1 and 3 also are undertaken. (v) In addition to the requirement in part (iv), assume that when projects 1 and 3 are undertaken, project 4 also must be undertaken.
Solution
(i) The constraint for this situation can be written as: x1 + x3 + x5 + x6 = 2. This means that out of projects 1, 3, 5, and 6, exactly two must be chosen.
(ii) The constraint for this situation can be written as: x3 - x5 = 0 and x5 - x3 = 0. This means that if project 3 is chosen, project 5 must also be chosen, and vice versa.
(iii) The constraint for this situation can be written as: x1 + x4 = 1. This means that either project 1 or project 4 must be chosen, but not both.
(iv) The constraints for this situation can be written as: x4 - x1 <= 0 and x4 - x3 <= 0. This means that project 4 can only be chosen if both projects 1 and 3 are chosen.
(v) The constraint for this situation can be written as: x1 + x3 - x4 = 0. This means that if projects 1 and 3 are chosen, project 4 must also be chosen.
Similar Questions
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