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 50 Wednesday 45 Thursday 70 Friday 100 Saturday 90 Sunday 60 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; = the number of call-center employees who start work on day i where i = 1 = Monday, i = 2 = Tuesday, etc). Min 110 Check the subscript of your variable(s). s.t. Monday 9565 Check which variable(s) should be in your answer. Tuesday 70 ≥35 × Check which variable(s) should be in your answer. Wednesday 5530 × Check which variable(s) should be in your answer. Thursday 5050 × Check which variable(s) should be in your answer. Friday 7575 Check which variable(s) should be in your answer. Saturday 90 90 × Check which variable(s) should be in your answer. Sunday 100 60 × Check which variable(s) should be in your answer. X₁₁ X1 X3 X4 X5, X6 X Find the optimal solution. (X1, X2 X3 X4 X5, X61 X7) = 25,0,0,35,40,15,10

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 50 Wednesday 45 Thursday 70 Friday 100 Saturday 90 Sunday 60 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; = the number of call-center employees who start work on day i where i = 1 = Monday, i = 2 = Tuesday, etc). Min 110 Check the subscript of your variable(s). s.t. Monday 9565 Check which variable(s) should be in your answer. Tuesday 70 ≥35 × Check which variable(s) should be in your answer. Wednesday 5530 × Check which variable(s) should be in your answer. Thursday 5050 × Check which variable(s) should be in your answer. Friday 7575 Check which variable(s) should be in your answer. Saturday 90 90 × Check which variable(s) should be in your answer. Sunday 100 60 × Check which variable(s) should be in your answer. X₁₁ X1 X3 X4 X5, X6 X Find the optimal solution. (X1, X2 X3 X4 X5, X61 X7) = 25,0,0,35,40,15,10

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 33E

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