3. (10') Consider a transportation problem with two supply modes and two demand nodes . ' The supply nodes have a and 107 _ " supplies respectively with O _ _ _ Loo ." The demand nodes require TO and all respectively . " The figure below illustrates the graph of the transportation problem . Let {; be the unit transportation cost from supply ; to demand ; . 1 = 1 1 - 2. Supply Demand E ! TO 100 - 8 30) ( a ) Write down a linear programming formulation of the above problem and present your A matrix . ( 6 ) Consider a spanning tree of the above graph generated by deleting the are ( 1 . 1 ) ( or forcing I'll = . Find the flow solution that satisfies all the flow- balancing constraints ( i.C., the solution to AX = $1