Boston's famous Limoges Restraurant is open 24 hours a day. Servers report for duty at 3 am, 7 am, 11 am, 3 pm, 7 pm, or 11 pm, and each works an 8 hour shift. The following table shows the minimum number of workers needed during the 6 periods into which the day is divided.
Period Time Number of servers required
1 3 AM - 7 AM 3
2 7 AM - 11 AM 12
3 11 AM - 3 PM 16
4 3 PM - 7 PM 9
5 7 PM - 11 PM 11
6 11 PM - 3 AM 4
Owner Michelle Limoges' scheduling problem is to determine how many servers should report for work at the start of each time period in order to minimize the total staff required for one day's operation. Formulate a linear programming model for this case.