a$)$ In XYZ distributors, operating in a county with four regions A$,$ B$,$ C$,$ and D$.$ customer demands and be met from three supply points; X$,$ Y and Z with capacities $50,60$ and $40$ respectively. The costs of transporting a unit from each supply point each destination are X$=(3,2,1,2),$ Y$=(1,4,3,1)$ and Z$=(4,2,3,2).$ In a given week the demand for the four regions were $20,50,40,$ and $20$ respectively.

i$)$ Formulate this into a transportation problem.