Question 3 (1Epsilon Airlines services predominately the eastern and south-eastern United States. The 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. 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. These estimates are as follows: Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Minimum number of employees needed 75 50 45 60 90 75 45 The call-center employees work five consecutive days and then have two consecutive days off. An employee may start 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. Formulate the LP model that will minimize the total number of call-center employees needed to meet the minimum requirements. (10 marks) (ii) The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows: Plant 1 2 3 1 4 8 5 Warehouse 2 7 5 Capacity 400 600 300 6 Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows: Customer Warehouse 1 2 3 4 1 6 4 8 4 2 3 6 7 7 Demand 300 300 300 400 Suppose that shipments between the two warehouses are permitted at $2 per unit and that direct shipments can be made from Plant 3 to Customer 4 at a cost of $7 per unit. Construct a transportation table for the transshipment problem. Then, formulate the LP model for the problem. (Hints: use P1, P2, and P3 to denote the plants, use W4 and W5 to denote the warehouses, and use C6, C7, C8, and C9 to denote the customers.) (15 marks)