The famous Y. S. Chang Restaurant is open 24 hours a day. Waiters and busboys report for duty at 3 A .M ., 7 A .M .,11 A .M ., 3 P .M ., 7 P .M ., or 11 P .M ., and each works an 8-hour shift. The following table shows the minimum number of workers needed during the six periods into which the day is divided. Chang's scheduling problem is to determine how many waiters and busboys should report for work at the start of each time period to minimize the total staff required for one day's operation. (Hint: Let equal the number of waiters and busboys beginning work in time period i , where i = 1, 2, 3, 4, 5, 6.)
NUMBER OF WAITERS
PERIOD TIME AND BUSBOYS REQUIRED
1 3 A.M.-7 A.M. 3
2 7 A.M.-11 A.M. 12
3 11 A.M.-3 P.M. 16
4 3 P.M.-7 P.M. 9
5 7 P.M.-11 P.M. 11
6 11 P.M.-3 A.M 4
(a) Add this additional constraint: Total Number of Workers to Start the Shifts must be less than or equal to 31.