409 (Algorithmic) Epsilon Airlines services predominately the eastern and southeastern United States. The vast majority of Epsilon's customers make reservations through Epsilon's website, but a small percentage of customers make reservations via phone. Epsilon employs callcenter personnel to handle these reservations along with any problems with the website reservation system and for the rebooking of flights for customers if their plans change or their travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon's management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers. Epsilon analysts have estimated the minimum number of callcenter employees needed by day of week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows: Minimum Number of Employees Needed 75 50 45 60 90 75 45 Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday The callcenter employees work five consecutive days and then have two consecutive days off. An employee may start work any day of the week. Each callcenter employee receives the same salary. Assume that the schedule cycles and ignore startup and stopping of the schedule. Develop a model that will minimize the total number of callcenter employees needed to meet the minimum requirements. Find the optimal solution. Give the number of callcenter employees that exceed the minimum required. Use Excel Solver. Let Xi = the number of call center employees who start work on day i (i = 1 = Monday, i = 2 = Tuesday...) Min s.t. X1 + X2 + X3 + X4 + X5 + X6 + X7 X1 + X4 + X5 + X6 + X7 X1 + X2 + X5 + X6 + X7 X1 + X2 + X3 X1 + X2 + X3 + X4 X1 + X2 + X3 + X4 + X5 + X6 + X7 + X7 X2 + X3 + X4 + X5 + X6 X3 + X4 + X5 + X6 + X7 X1, X2, X3, X4, X5, X6, X7 0 Solution: X1 = X2 = X3 = X4 = X5 = X6 = X7 = Number of excess employees: Monday = Tuesday = Wednesday = Thursday = Friday = Saturday = Sunday = Total Number of Employees =