Problem 2 (11 points)

The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows.

Plant	Warehouse		Capacity
	1	2
1	4	7	450
2	8	5	600
3	5	6	380

Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows.

Formulate a linear programming model of the problem. (Let Plant 1 be node 1, Plant 2 be node 2, Plant 3 be node 3, Warehouse 1 be node 4, Warehouse 2 be node 5, Customer 1 be node 6, Customer 2 be node 7, Customer 3 be node 8, and Customer 4 be node 9.

Warehouse	Customer
	1	2	3	4
1	6	4	8	4
2	3	6	7	7
Demand	300	300	300	400

Define the decision variables. (1 point)

Define the objective function (2 points)

Define the constraints (5 points)

Determine an optimal solution (3 points)