$5.($a$)$ Anita is the logistics manager for a company that produces and delivers bottled water

to several cities. The company has three bottling plants, located in City A$,$ City B$,$ and

City $C,$ and six delivery locations, located in City D$,$ City E$,$ City F$,$ City G$,$ City H$,$ and

City I. The following table shows the capacities of the pipelines that connect the

bottling plants to the delivery locations:

Page $4$ of $6$

Anita wants is to determine the maximum number of gallons of bottled water that can

be transported from the bottling plants to the delivery locations. Present a graphical

representation of the problem Anita is trying to solve. Then formulate an optimization

model for it$.$