A linear programming computer package is needed.

Epsilon Airlines services predominately the eastern and southeastern United States. A vast majority of Epsilon's customers make reservations through Epsilon's website, but a small percentage of customers make reservations via phone. Epsilon employs call-center 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 call-center employees needed by day of week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are given in the following table.

Day	Minimum Number of Employees Needed
Monday	80
Tuesday	55
Wednesday	50
Thursday	65
Friday	95
Saturday	75
Sunday	40

The call-center employees work five consecutive days and then have two consecutive days off. An employee may start work any day of the week. Each call-center employee receives the same salary. Assume that the schedule cycles and ignore start-up and stopping of the schedule. Develop a model that will minimize the total number of call-center employees needed to meet the minimum requirements. (Let X_i = the number of call-center employees who start work on day i where

i = 1 = Monday, i = 2 = Tuesday, etc).

Min x1+x2+x3+x4+x5+x6+x7

s.t.

Monday. X1+X4+X5+X6+X780

Tuesday. X1+X2+X5+X6+X755

Wednesday X1+X2+X3+X6+X750

Thursday. X1+X2+X3+X4+X765

Friday X1+X2+X3+X4+X595

Saturday. X2+X3+X4+X5+X675

Sunday X3+X4+X5+X6+X740

X₁, X₂, X₃, X₄, X₅, X₆, X₇ 0

Find the optimal solution.

(X₁, X₂, X₃, X₄, X₅, X₆, X₇) = ?

Give the number of call-center employees that exceed the minimum required.

(M, Tu, W, Th, F, Sa, Su) = ?