The following questions refer to a project selection problem with six projects r

Question

The following questions refer to a project selection problem with six projects represented by binary variables x1, x2, x3, x, xs, andx a) Write a constraint modeling a situation in which at least two of the projects 1, 3, 5, and 6 must be undertaken. b) Write a constraint modeling a situation in which project 1 or 4 must be undertaken, but c) Write a constraint modeling a situation in which project 4 cannot be undertaken unless d) Write a constraint modeling a situation in which, if projects 1 and 3 are both undertaken, not both projects 1 and 3 are also undertaken. then project 6 must also be undertaken. (e) At least one of the following two conditions need to be satisfied: .3x1 5x2 + 4x3 + 6x4 +xs+2x6 S9 How would you represent this requirement using linear constraints (and an additional binary decision variables)?

Explanation / Answer

a) x1+ x3 + x5 +x6 =2

b) x1 +x4 =1

c) x4 < x1

x4 < x3

d)   x6 < x1

x6 < x3

x6 > x1+x3-1

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