Six urban planners—P, Q, R, S, T, and U—are to be assigned to two project groups, Group Alpha and Group Beta, such that each group contains exactly three members. The assignment must strictly comply with the following conditions:
1. Planner R must be assigned to Group Alpha.
2. Planners P and Q cannot be in the same group.
3. Planners S and T must be assigned to the same group.
4. Planner U cannot be assigned to Group Beta unless planner S is also assigned to Group Beta.
Which of the following statements regarding the group assignments are definitely correct?
- Planner U must be assigned to Group Alpha.Cevap
- Both planners S and T must be assigned to Group Beta.Cevap
- CPlanner P and planner R must always be assigned to the same group.
- DPlanners U and S can be assigned to the same group.
Cevap
Planner U must be assigned to Group Alpha, and both planners S and T must be assigned to Group Beta.
Group Alpha starts with planner R and gets exactly one of P or Q, leaving only one open slot. Planners S and T must be in the same group, requiring two open slots, so they must be placed in Group Beta. This completely fills Group Beta with three members (S, T, and one of P or Q), forcing planner U into Group Alpha. Therefore, the statements that planner U must be in Group Alpha and that both S and T must be in Group Beta are unequivocally correct.
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Anahtar Kavram
Analytical Grouping and Capacity Constraints