Cars are shipped from three distribution centers to five dealers. The shipping cost is

based on the mileage between the sources and the destinations and is independent of whether the truck makes the trip with partial or full loads. Table $5\mathrm{.}28$ summarizes the mileage between the distribution centers and the dealers together with the monthly supply and demand figures given in number of cars. A full truckload includes $18$ cars. The transportation cost per truck mile is $$25.$

$($a$)$ Formulate the associated transportation model.

$($b$)$ Determine the optimal shipping schedule.