Bank 24 is open 24 hours per day. Tellers work two consecutive 6-hour shifts and are paid $10 per hour. The possible shifts are as follows: midnight–6 a.m., 6 a.m.–noon, noon–6 p.m., 6 p.m.–midnight. During each shift, the following numbers of customers enter the bank; midnight 6 a.m., 100; 6 a.m.–noon, 200; noon–6 p.m., 300; 6 P.M.–midnight, 200. Each teller can serve up to 50 customers per shift. To model a cost for customer impatience, we assume that any customer who is present at the end of a shift “costs” the bank $5. We assume that by midnight of each day, all customers must be served, so each day’s midnight–6 a.m. shift begins with 0 customers in the bank. Formulate an LP that can be used to minimize the sum of the bank’s labor and customer impatience costs.
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