Instructions:

1. For each problem, please come up with a LP formulation (decision variables, objective function, and constraints) with clearly defined decision variables, an objective function, and constraints.
2. Solve each problem by Excel. Make sure to pay attention on the problem representation and layout. You also need to follow the color scheme (data-green, decision variable-blue, objective function-red, formula-black).

Question:

Arlington Bank of Commerce and Industry is a busy bank that has requirements for between 10 and 18 tellers depending on the time of day. The lunch time, from noon to 2pm, is usually heaviest. The following table indicates the workers needed at various hours that the bank is open.

Time Period	9-10	10-11	11-12	12-1	1-2	2-3	3-4	4-5
# of tellers needed	10	12	14	16	18	17	15	10

The bank now employs 12 full-time tellers, but many people are on its roster of available part-time employees. A part-time employee must put in exactly four hours per day, but can start anytime between 9am and 1pm. Part-time is fairly inexpensive labor pool, since no retirement or lunch benefits are provided them. Full-timers, on the other hand, work from 9am-5pm, but are allowed an hour for lunch. (Half of the full-timers eat at 11am, the other half at noon.) Full-timers thus provide 35 hours per week of productive labor time. By corporate policy, the bank limits part-time hours to a maximum of 50% of the day's total requirement. Part-timers earn $4 per hour (or $16 per day) on the average, while full-timers earn $50 per day in salary and benefits, on the average. The bank would like to set a schedule that would minimize its total personnel costs. It will release one or more of its full-time tellers if it is profitable to do so. Provide your recommendations to the Bank.