$4-$ The network in the following figure shows the routes for shipping cars from three plants $($nodes

$1,2,$ and $3)$ to three dealers $($nodes $6,7$ and $8)$ by way of two distribution centers $($nodes $4$ and $5).$ The

shipping costs per car $($in $$100)$ are shown on the arcs.

a$.$ Solve the problem as a transshipment model.

b$.$ Find the new optimum solution if the distribution center $4$ can sell $240$ cars directly to

customers.