FizeauV

2021-03-11

Consider a capital budgeting problem with seven projects represented by binary (0 or 1) variables ${X}_{1},\text{}{X}_{2},\text{}{X}_{3},\text{}{X}_{4},\text{}{X}_{5},{X}_{6},{X}_{7}$ .
Write a constraint modeling the situation in which only 2 of the projects from $1,\text{}2,\text{}3\text{}and\text{}4$ must be selected.
Write a constraint modeling the situation in which at least 2 of the project from $1,\text{}3,\text{}4,\text{}and\text{}7$ 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.

Caren

Skilled2021-03-12Added 96 answers

Step 1
Write a constraint modelling the situation in which only 2 of the projects from $1,\text{}2,\text{}3,\text{}and\text{}4$ must be selected
Therefore, the constraint is,
${X}_{1}\text{}+\text{}{X}_{2}\text{}+\text{}{X}_{3}\text{}+\text{}{X}_{4}=2$
Step 2
Write a constraint modelling the situation which at least 2 of the projects from $1,\text{}3,\text{}4\text{}and\text{}7$ must be selected
Therefore, the constraint is,
${X}_{1}\text{}+\text{}{X}_{3}\text{}+\text{}{X}_{4}\text{}+\text{}{X}_{7}\ge \text{}2$
Step 3
Write a constraint modelling the situation project 3 or 6 must be selected, but not both.
Therefore, the constraint is,
${X}_{3}\text{}+\text{}{X}_{6}=1$
Step 4
Write a constraint modelling the situation in which at most 4 projects from the 7 can be selected.
Therefore, the constraint is,
${X}_{7}\le \text{}4$

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