Problem:

Each hour from 10 A.M. to 7 P.M., First National Bank of Gainesville receives checks and must eventually process them. Its goal is to process all checks the same day they are received. The bank currently has 20 check processing machines, each of which can process up to 400 checks per hour. It takes one worker to operate each machine. This bank hires both full-time and part-time workers. Full-time employees work 10 A.M. to 6 P.M., 11 A.M. to 7 P.M., OR noon to 8 P.M., and are paid $180 per day. Part-time employees work either 2 P.M. to 7 P.M. OR 3 P.M. to 8 P.M., and are paid $90 per day. The number of checks typically received each hour is 2500 between 10-11, 3000 between 11-N, 3500 between N-1, 4000 between 1-2, 4500 between 2-3, 5000 between 3-4, 4500 between 4-5, 4000 between 5-6, 3500 between 6-7, and 3000 between 7-8.

Required:

Formulate and solve a linear programming model in Excel to develop a work schedule that processes all checks by 8 P.M. and minimizes daily labor costs.

Provide detailed explanation of the given problem.