The North Shore Bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank, including adequate customer service and employee breaks. The bank is open from 9:00 a.m. to 7:00 p.m. The number of tellers necessary to provide adequate customer service during each hour of operation is as follows:

Time	No. of Tellers
9:00 a.m.10:00 a.m.	6
10:00 a.m.11:00 a.m.	4
11:00 a.m.Noon	8
Noon1:00 p.m.	10
1:00 p.m.2:00 p.m.	9
2:00 p.m.3:00 p.m.	6
3:00 p.m.4:00 p.m.	4
4:00 p.m.5:00 p.m.	7
5:00 p.m.6:00 p.m.	6
6:00 p.m.7:00 p.m.	6

Each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost the bank $8 per hour ($32 per day).

The bank manager also needs to ensure that one full-time employee is on duty at all times and that there is a staff of at least five full-time employees.

Develop an integer linear optimization model to determine how many of each type of employee should start working at each of the 10 hours of operation.

a) What is the bank's lowest total cost?

b) How many full-time employees should start working at 10am?

c) How many full-time employees should be working during 10am to 11am?

d) How many part-time employees should start working at 10am?

e) How many part-time employees should be working during 10am to 11am?