Hong Kong Bank of Commerce and Industry is a busy bank that has requirements for between 10 and 18 tellers, depending on the time of day. The lunch time, from noon to 2 p.m., is usually heaviest. The following table shows the workers needed at various hours that the bank is open.

Time Period	No. of Tellers Required
9 a.m.--10 a.m.	10
10 a.m.--11a.m.	12
11 a.m.--Noon	14
Noon--1 p.m.	16
1 p.m.--2 p.m.	18
2 p.m.--3 p.m.	17
3 p.m.--4 p.m.	15
4 p.m.--5 p.m.	10

The bank now employs 12 full-time tellers, but many people are on its roster of available part-time employees. A part-time employee must put in exactly 4 hours per day but can start anytime between 9 a.m. and 1 p.m. Part-timers are fairly inexpensive labor pool, since no retirement or lunch benefits are provided for them. Full-timers, on the other hand, work from 9 a.m. to 5 p.m. but are allowed 1 hour for lunch. (Half of the full-timers eat at 11 a.m., the other half at noon.) Full-timers thus provide 35 hours per week of productive labor time.

By corporate policy, the bank limits part-time hours to a maximum of 50% of the day's total requirement. Part-timers earn $4 per hour (or $16 per day) on average, and full-timers earn $50 per day in salary and benefits, on average. The bank would like to set a schedule that would minimize the total personnel costs. It will release one or more of its full-time tellers if it is possible to do so. It is your job to help the bank determine the schedule.

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