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.DayMinimum Number ofEmployees NeededMonday70Tuesday50Wednesday45Thursday60Friday90Saturday80Sunday50The 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 Xi = the number of call-center employees who start work on day i where i = 1 = Monday, i = 2 = Tuesday, etc).Min Z=x1+x2+x3+x4+x5+x6+x7 Check which variable(s) should be in your answer.s.t.Mondayi1+i4+i5+i6+i7≥70 Check which variable(s) should be in your answer.Tuesday50 Enter inequalities using less than (<), greater than (>), less than or equal (≤), or greater than or equal (≥).Wednesday Thursday Friday Saturday SundayX3+X4+X5+X6+X7>=50 X1, X2, X3, X4, X5, X6, X7 ≥ 0Find the optimal solution.(X1, X2, X3, X4, X5, X6, X7) = 15 Give the number of call-center employees that exceed the minimum required.(M, Tu, W, Th, F, Sa, Su) = 0,0,0,30,0,0,5

Linear programming is a mathematical technique that is also used in operations management…

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 59P

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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	70
Tuesday	50
Wednesday	45
Thursday	60
Friday	90
Saturday	80
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. (Let

X_i

= the number of call-center employees who start work on day i where

i = 1 = Monday,

i = 2 = Tuesday,

etc).

Min

Z=x1+x2+x3+x4+x5+x6+x7

Check which variable(s) should be in your answer.

s.t.Monday

i1+i4+i5+i6+i7≥70

Check which variable(s) should be in your answer.Tuesday

Enter inequalities using less than (<), greater than (>), less than or equal (≤), or greater than or equal (≥).Wednesday

Thursday

Friday

Saturday

Sunday

X3+X4+X5+X6+X7>=50

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) =

0,0,0,30,0,0,5

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