Problem $9-09($Algorithmic$)$ Find the optimal solution.

Total Number of Employees $=$

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

Excess employees:

Epsilon Airlines services predominantly 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 phones. Epsilon employs call center personnel to handle these reservations and to deal with website

reservation system problems and for the rebooking of flights for customers whose plans have changed or whose 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 the week for the upcoming vacation season $($June$,$ July, and the first

two weeks of August$).$ These estimates are as follows:

The call center employees work for five consecutive days and then have two consecutive days off. An employee may start work on any day of the week. Each caller

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

$(i=1=$ Monday, $i=2=$ Tuesday dots$)$

$Min{x}_1+x_2+x_3+x_4+x_5+x_6+x_7$

s$.$t$.$