$(34$ 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.

$\backslash$table$[[,$Retail Stores,Supply$],[\backslash$table$[[$Distribution$],[$Centers$]],,$A$,$B$,$C$],[1,5,8,7,150],[2,4,7,5,130],[,3,6,5,4,140],[$Demand$,50,70,60,]]$

Formulate the problem as a binary integer programming problem. $($DO NOT solve the problem$).$