Epsilon Airlines services predominately the eastern and southeastern United States. A vast majority of Epsilons customers make reservations through Epsilons 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 Epsilons 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 as follows:

	Minimum Number of
Day	Employees Needed
Monday	60
Tuesday	60
Wednesday	50
Thursday	75
Friday	45
Saturday	60
Sunday	50

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. Find the optimal solution and determine the total number of call-center employees under the optimal solution. Use a software package LINGO or Excel Solver. If your answer is zero, enter "0".

Let X_i = the number of call center employees who start work on day i (i = 1 = Monday, i = 2 = Tuesday)

Min

X1

+

X2

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X3

+

X4

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X5

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X6

+

X7

s.t.

fill in the blank X1

+

fill in the blank X2

+

fill in the blank X3

+

fill in the blank X4

+

fill in the blank X5

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fill in the blank X6

+

fill in the blank X7

=

fill in the blank

fill in the blank X1

+

fill in the blank X2

+

fill in the blank X2

+

fill in the blank X2

+

fill in the blank X5

+

fill in the blank X6

+

fill in the blank X7

=

fill in the blank

fill in the blank X1

+

fill in the blank X2

+

fill in the blank X3

+

fill in the blank X4

+

fill in the blank X5

+

fill in the blank X6

+

fill in the blank X7

=

fill in the blank

fill in the blank X1

+

fill in the blank X2

+

fill in the blank X3

+

fill in the blank X4

+

fill in the blank X5

+

fill in the blank X6

+

fill in the blank X7

=

fill in the blank

fill in the blank X1

+

fill in the blank X2

+

fill in the blank X3

+

fill in the blank X4

+

fill in the blank X5

+

fill in the blank X6

+

fill in the blank X7

=

fill in the blank

fill in the blank X1

+

fill in the blank X2

+

fill in the blank X3

+

fill in the blank X4

+

fill in the blank X5

+

fill in the blank X6

+

fill in the blank X7

=

fill in the blank

fill in the blank X1

+

fill in the blank X2

+

fill in the blank X3

+

fill in the blank X4

+

fill in the blank X5

+

fill in the blank X6

+

fill in the blank X7

=

fill in the blank

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 Under the Optimal Solution=