Question

2. The following questions refer to a capital budgeting problem with six projects represented by binary variables a, b, c, d, e, and f. a. Write a constraint modeling a situation in which two of the projects 1, 3, 5, and 6 must be undertaken. b. Write a constraint modeling a situation in which, if project 3 or 5 is undertaken, they must both be undertaken. c. Write a constraint modeling a situation in which project 1 or 4 must be undertaken, but not both. d. Write constraints modeling a situation where project 4 cannot be undertaken unless projects 1 and 3 are also undertaken. e. Revise the requirement in part (d) to accommodate the case in which, when projects 1 and 3 are undertaken, project 4 must also be undertaken.

Answer 1

Pg Noro cal e to or Answert A capital budgeting problem with six projects represented by binary vanables a,b,c,d,e and P. @ As of the 4 projects will be undertaken, & variables will be I and I will be o. Hence, the constraint will be atct effaf 6 af project is and 5 are both taken they will be and both are excluded they will be o. it cannot be that and (0 and eat so, constraint will be acce 1-1 0 © As only one of the projects 1,4 will be undertaken, either of a ord will be l. constraint will be atdal ① Project 4 will be undertaken only if 1 and 3 are also undertaken. a cannot be more than a and c. In other words, d = 1 only a=l and cal. This constraints are: d<=Q , dczc. first . 2 constraints will be the same as in "d" above. dz=Q, dasci Also if a=1 and cal, then d will also be i (it can't be o then). So, the 3rd constraint will be d>=Q+cal. @ The