$2.(34$ pts$.)$ A multinational company is planning to optimize its logistics network by deciding which of its $3$ potential distribution centers $(1,2,3)$ to open, and how much to ship from each distribution center to $3$ retail stores $($A$,$ B$,$ C$).$ The company incurs fixed opening costs for distribution centers $1,2,$ and $3,$ at the rate of $$100,$ $$800$ and $$900$ respectively. The unit transportation costs from the distribution centers to retail stores, supply capacities from distribution centers $1,2,3,$ and demand units from retail stores A$,$ B$,$ and C are given in the following table. The company is willing to open maximum of two distribution centers