Exercise 3

Exercise 3 (45 points) NTC is a small business that receives checks from all over Cote d'Ivoire. The average daily total payments mailed by customers from each region of Cote d'Ivoire to NTC is as follows: the West, 70000 CFA Francs; the North, 50000 CFA Francs; the East, 40000 CFA Francs; the South, 60000 CFA Francs. NTC must decide where customers should mail their payments. Because NTC can earn 20% annual interest by investing these revenues, NTC would like to receive payments as quickly as possible. NTC is considering setting up operations to process payments in four cities: Abidjan, Abengourou, Korhogo, and Man. The average number of days from the time the is sent until it is cleared and deposited in NTC bank account depends on the city to which the payment is mailed, as shown in the table below. City 4 City 1 Man 2 6 Region 1: West Region 2: North Region 3: East Region 4: South O O ON City 2 Korhogo 6 2 5 5 u UNO City 3 Abengourou 8 5 2 5 No 0 Abidjan 8 5 5 2 Non 8 The annual cost for the payment processing office in a city is 50000 CFA Francs. In addition, if customers in Region 1 (West) send their checks to City 1 (Man), then no other customers from the other regions may sent their payments to City 1. 1. Formulate an Integer Programming model that NTC can use to minimize the sum of the costs due to lost interest income and running a payment processing office. 2. Use MS Excel to find the optimal solution to this IP