Formulate an integer programming model that determines which facilities to keep open, which facilities to close and the amount of transported computers from facilities to customers with a minimum cost.

A computer manufacturer in the USA has 5 major customers (A, B, C, D, E) and currently has 6 computer 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 D E Annual Supply Fixed Cost Capacity Facility 1 $1 $3 $5 $6 $4 $3000 300 Facility 2 2 5 7 4 3 4000 300 Facility 3 8 5 3 2 1 3500 300 Facility 4 1 5 7 2 3 4200 300 Facility 5 5 3 2 4 8 3800 300 Facility 6 4 2 5 6 8 3700 300 Demand 200 200 220 200 230 The car manufacturer company considers the following condition in their planning Either facility 1 or facility 3 must be open. If facility 5 is operating then facility 6 must be used. At most 5 facilities must be open. At least 3 facilities must be open. Due to cost related conditions, the company cannot select facility 2 and facility 4 at the same time