Nash Auto has two plants (node numbers 1 and 2), two warehouses (node numbers 3 and 4), and two customers (node numbers 5 and 6). Cars are produced at plants, then shipped to customers directly or warehouses, and finally sent to customers. Plant 1 produces 300 cars per week, and Plant 2 produces 400 cars per week. Customer 1 (node number 5) requires 250 cars per week, and customer 2 (node number 6) needs 150 cars. The costs of shipping a vehicle between nodes are listed in the table. Define the decision variables such as Xij = number of cars shipped from node i to node j (i=1,2,3,4 and j=2,3,4,5,6).

a)Define the constraint for Node 1 (Plant 1),b)Define the constraint forNode 4 (Warehouse 2)

C)Define the constraint forNode 6 (Customer 2)

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