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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 B c D E Annual Supply Fixed Cost Capacity Facility 1 $1 $3 $5 $6 S4 $2000 150 Facility 2 2 5 7 4 3 3000 150 Facility 3 8 5 3 2 1 2500 150 Facility 4 1 5 7 2 3 3200 150 Facility 5 5 3 2 4 8 2800 150 Facility 6 4 2 5 6 8 2700 150 Demand 100 100 120 100 130 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 !)