management science/integer programming model

A car manufacturer in Turkey has 5 major customers (A, B, C, D, E) and currently has 6 car manufacturing facilities. The company decides to keep some of those facilities operating and some of them shutting down. The transportation costs, annual fixed costs, supply capacities and demands are given the table below: A A B D E Annual Fixed Cost Facility $1 $3 $5 $6 $4 $2000 1 Facility 2 5 7 4 3 3 3000 2 2 Facility 8 8 5 3 3 N 1 2500 3 Facility 1 1 5 5 7 2 3 3200 4 Facility 5 3 2 4 8 B 2800 5 Facility 4 4 2 5 5 6 8 8 2700 6 Demand 100 100 120 100 130 ,, B, C, D, E) and currently has 6 car g facilities. The company decides to f those facilities operating and some ing down. The transportation costs, costs, supply capacities and given the table below: B B 10 10 15 Annual Supply Fixed Capacity Cost 1 $3 $5 $6 $4 $2000 150 07 7 7 4 3 3000 150 5 3 2 2 1 2500 150 5 5 7 2 3 3 3200 150 3 2 4 8 8 2800 150 2 2 01 5 6 8 2700 150 00 100 120 100 130 The car manufacturer company considers the following condition in their planning: Either facility 1 or facility 2 must be open. If facility 4 is operating then facility 6 must be used. At most 5 facilities must be open. Due to geographical conditions, the company cannot select facility 1 and facility 3 at the same time. Formulate an integer programming model that determines which facilities to keep open, which facilities to close and the amount of transported cars from facilities to customers with a minimum cost. (do not solve the problem, define an integer model !)