Consider a capital budgeting problem with seven projects represented by binary (0 or 1) variables X_{1}, X_{2}, X_{3}, X_{4}, X_{5}, X_{6}, X_{7}. Write a constraint modeling the situation in which only 2 of the projects from 1, 2, 3 and 4 must be selected. Write a constraint modeling the situation in which at least 2 of the project from 1, 3, 4, and 7 must be selected. Write a constraint modeling the situation project 3 or 6 must be selected, but not both. Write a constraint modeling the situation in which at most 4 projects from the 7 can be selected.

Consider a capital budgeting problem with seven projects represented by binary (0 or 1) variables X_{1}, X_{2}, X_{3}, X_{4}, X_{5}, X_{6}, X_{7}. Write a constraint modeling the situation in which only 2 of the projects from 1, 2, 3 and 4 must be selected. Write a constraint modeling the situation in which at least 2 of the project from 1, 3, 4, and 7 must be selected. Write a constraint modeling the situation project 3 or 6 must be selected, but not both. Write a constraint modeling the situation in which at most 4 projects from the 7 can be selected.

Question
Modeling
asked 2021-03-11
Consider a capital budgeting problem with seven projects represented by binary (0 or 1) variables \(X_{1},\ X_{2},\ X_{3},\ X_{4},\ X_{5}, X_{6}, X_{7}\). Write a constraint modeling the situation in which only 2 of the projects from \(1,\ 2,\ 3\ and\ 4\) must be selected. Write a constraint modeling the situation in which at least 2 of the project from \(1,\ 3,\ 4,\ and\ 7\) must be selected. Write a constraint modeling the situation project 3 or 6 must be selected, but not both. Write a constraint modeling the situation in which at most 4 projects from the 7 can be selected.

Answers (1)

2021-03-12
Step 1 Write a constraint modelling the situation in which only 2 of the projects from \(1,\ 2,\ 3,\ and\ 4\) must be selected Therefore, the constraint is, \(X_{1}\ +\ X_{2}\ +\ X_{3}\ +\ X_{4} = 2\) Step 2 Write a constraint modelling the situation which at least 2 of the projects from \(1,\ 3,\ 4\ and\ 7\) must be selected Therefore, the constraint is, \(X_{1}\ +\ X_{3}\ +\ X_{4}\ +\ X_{7} \geq\ 2\) Step 3 Write a constraint modelling the situation project 3 or 6 must be selected, but not both. Therefore, the constraint is, \(X_{3}\ +\ X_{6} = 1\) Step 4 Write a constraint modelling the situation in which at most 4 projects from the 7 can be selected. Therefore, the constraint is, \(X_{7} \leq\ 4\)
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