The demand in all branches of banks varies during the day. The AIBC International branch in Toronto has a peak demand for domestic transactions around lunchtime. When this is translated into the number of employees needed in the branch, it gives the following pattern. This demand is met by a combination of normal work by full-time staff and overtime by full-time staff and part-time staff. Approximate hourly costs for these are $20, $25 and $15 respectively. The bank aims to provide at least the number of people required at minimum cost. But there are a number of constraints.
These include:
The bank does not work outside the 0900 to 1900 time slot.
Full-time staff are available for 35 hours a week, and anything beyond this is overtime.
Full-time staff rarely like to work more than 5 hours of overtime a week.
All full-time staff have an hour's lunch break at an agreed time between 1100 and 1300.
Part-time staff work between 4 and 8 hours a day without a lunch break.
A company policy limits part-time staff to a maximum of 40% of hours worked.
Can LP tackle this kind of schedulingproblem?

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Number of Period Number of employees Period employees 0900-1000 1000-1100 1100-1200 1200-1300 1300-1400 20 35 40 55 75 1400-1500 1500-1600 1600-1700 1700-1800 1800-1900 85 70 45 20 10