Scheduling Peer Tutoring Sessions
An after-school tutoring center has three volunteer tutors and six student requests for next Saturday. Each session lasts one hour. Tutor A is available 09:00-12:00 and can tutor math and chemistry. Tutor B is available 10:00-13:00 and can tutor math and physics. Tutor C is available 09:00-11:00 and can tutor chemistry and biology. Requests: R1 math, R2 physics, R3 chemistry, R4 biology, R5 math, R6 chemistry. Each tutor can teach at most one student per hour slot, and each student needs exactly one hour. R1 and R5 are siblings and must be scheduled at different times so a parent can drive them. R2 must be before 11:00 because the student has a match at 11:30. R3 can only come at 10:00 or later. The center director wants to know whether all six requests can be met with the current volunteer availability. If not, which single request should be referred to another center, and why?
1. Determine whether all six requests can be scheduled. Show a feasible schedule or prove infeasibility.
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Yes, all six can be scheduled. One feasible schedule:
- 09:00: Tutor A - R1 (math); Tutor C - R4 (biology).
- 10:00: Tutor A - R6 (chemistry); Tutor B - R2 (physics); Tutor C - R3 (chemistry).
- 11:00: Tutor B - R5 (math). Checks: R1 and R5 are at different times (09:00 and 11:00). R2 is before 11:00. R3 is at 10:00. Tutor qualifications match: A can do math/chemistry, B math/physics, C chemistry/biology. Each tutor has at most one student per slot.
2. Suppose Tutor C becomes unavailable. Can the remaining five requests (R1-R5) still be scheduled? If not, which request should be referred out?
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Without Tutor C, R4 (biology) cannot be scheduled because C is the only tutor qualified in biology. Refer R4. The remaining five can be scheduled: R2 (B, 10:00), R1 (A, 09:00), R5 (B, 11:00), R3 (A, 10:00), and R6 (A, 11:00). Check R1/R5 different times: 09:00 vs 11:00. R2 before 11:00: yes. R3 at 10:00 or later: yes. So the single referral should be R4.