8-3 (Restaurant work scheduling problem). 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 Xi equal the
number of waiters and busboys beginning work in
time period i, where i = 1, 2, 3, 4, 5, 6.)

PERIOD TIME NUMBER OF WAITERS 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

* ADDITIONAL CONSTRAINT Total number of workers to start the shifts must be less less than or equal to 31.

Please need help fast. my due date is tomorrow. Thank you,