Problem $4$: Trinity Auto Restorations purchases $18$ used vehicles from two vehicle suppliers everyweek, located in different cities. The vehicles are then transported to two

restoration centers contracted by Trinity Auto for repairs. After restoration, the vehicles are transported to three dealerships for sale. Each supplier has a specific supply limit$,$

and each dealership has a demand for a certain number of vehicles. However, there are no capacity restrictions at the restoration centers

everything that arrives at a restoration center must be processed and sent to the dealerships. The transportation costs between the suppliers, restoration centers, and dealerships are shown in the tables belov

Supply and Demand:

Supplier $1$:$18$ vehicles available

Supplier $2$: $18$ vehicles available

Dealership $1$: Requires $10$ vehicles

Dealership $2$: Requires $10$ vehicles

Dealership $3$: Requires $16$ vehicles

Problem:

a$.$ Draw a network representation of this transshipment problem, labeling all arcs and nodes, and marking supply, demand, and transportation costs.

b$.$ Write the linear programming $($LP$)$ model for this problem.

c$.$ Solve this transshipment problem and determine the minimum transportation cost.