The Northshore Banks working to develop an efficient work schedule for full-time and part-time teller. The schedule must provide for efficient operation of the bank including adequate customer service, employee breaks and so on. The bank is open from 9am to 5pm. The number of tellers necessary to provide adequate customer service during each hour of operation is summarised here.

Time	Number of Helpers
9am-10am	8
10am-11am	8
11am-12pm	8
12pm 1pm	6
1pm 2pm	6
2pm 3pm	5
3pm 4pm	5
4pm 5pm	7

There are three full-time tellers come to help; and two come at 10am and work a 4 hours shift, followed by 1-hour break, and continually until 5pm. Meanwhile, one comes a 12pm and works for 3 hours. In other hands, the part time tellers will work for 3-hour shift beginning on the hour except for those starting at 2pm and 3pm who will work for 2-hour only.

1. Formulate and determine an optimal schedule for the part time helpers.
2. You realised that full time staff should not be considered in the allocation and suggest the part time teller to work for 4-hour shift. Revise the model in (a) to determine whether your suggestion is better than the schedule in part (a).