Mexico City Bank of Commerce and Industry is a busy bank that has requirements for between 10

Question:

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

image text in transcribed

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 a fairly inexpensive labor pool because no retirement or lunch benefits are provided them. Full-timers, on the other hand, work from 9 a.m. to 5 p.m. but are allowed 1 hour for lunch. (Half 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 $6 per hour (or $24 per day) on average, whereas full-timers earn $75 per day in salary and benefits on average.
APPROACH c The bank would like to set a schedule, using LP, that would minimize its total manpower costs. It will release 1 or more of its full-time tellers if it is profitable to do so.
We can let:
F = full-time tellers P1 = part-timers starting at 9 a.m. (leaving at 1 p.m.)
P2 = part-timers starting at 10 a.m. (leaving at 2 p.m.)
P3 = part-timers starting at 11 a.m. (leaving at 3 p.m.)
P4 = part-timers starting at noon (leaving at 4 p.m.)
P5 = part-timers starting at 1 p.m. (leaving at 5 p.m.)