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.