A furniture manufacturer has warehouses in cities represented by nodes 1, 2, and 3 in the figure below. The values on the arcs indicate the per unit shipping costs required to transport living room suites between the various cities. The supply of living room suites at each warehouse is indicated by the negative number next to nodes 1, 2, and 3. The demand for living room suites is indicated by the positive number next to the remaining nodes. (Let X_ij represent the number of units that flow from node i to node j.)

(a)

Identify the supply nodes in this problem. (Enter your answers as a comma-separated list.)

Identify the demand nodes in this problem. (Enter your answers as a comma-separated list.)

Identify the transshipment nodes in this problem. (Enter your answers as a comma-separated list.)

(b)

What is the least costly shipping plan for this problem?

(X₁₃, X₁₄, X₂₄, X₂₅, X₃₄, X₃₆, X₄₆, X₅₄, X₅₆) =