The Op-Shop Roster
A community op-shop has two volunteers on the floor each weekday morning. The manager leaves a note: "Sam can only work Monday and Wednesday. Priya cannot work Fridays. Jo can work any day except Tuesday. We need two different people each morning from Monday to Friday, and nobody works more than two mornings a week."
A new volunteer, Lee, arrives and offers to work Friday only. The manager also wants every volunteer to have at least one morning off. Sam has a dentist appointment on Wednesday and now cannot work that day.
1. Can the shop still be staffed with two people every weekday morning? Explain using the constraints.
Read the worked answer
Work through each day after Sam loses Wednesday.
- Monday: Sam plus either Priya or Jo.
- Tuesday: Jo is out, so it must be Priya plus Lee? Lee only offered Friday, so Tuesday needs Priya and Sam - but Sam is only free Monday now. This is the problem.
Check who is available Tuesday: Priya yes, Jo no, Sam no, Lee no. Only one person, so Tuesday cannot be covered.
Answer: No. Tuesday fails because Jo is unavailable and Sam can no longer help, leaving only Priya. The manager must either ask Jo to work Tuesday or ask Lee to cover a second day.
2. If Jo agrees to work Tuesday, does the "no more than two mornings" rule still hold? Show a workable roster.
Read the worked answer
Build a roster respecting the two-morning cap.
- Monday: Sam, Priya
- Tuesday: Jo, Priya
- Wednesday: Priya, Jo
- Thursday: Sam, Jo
- Friday: Sam, Lee
Count mornings: Sam = Mon, Thu, Fri = 3. That breaks the cap.
Adjust: move Sam off Thursday.
- Monday: Sam, Priya
- Tuesday: Jo, Priya
- Wednesday: Priya, Jo
- Thursday: Jo, Lee? Lee only offered Friday.
So Thursday needs two from Sam, Priya, Jo. Priya already has Mon, Tue, Wed = 3, over the cap.
Answer: With only four volunteers and these limits, the two-morning cap cannot be met every day. Something must give - likely Priya's cap or Lee's single-day offer.