The blood bank wants to determine the least expensive way to transport available blood donations from Pittsburgh and Staunton to hospitals in Charleston, Roanoke, Richmond, Norfolk, and Suffolk. The supply and demand for donated blood is shown in the figure below along with the unit cost of shipping along each possible arc. The goal is to meet the expected demand at the lowest possible cost. (Let X_ij represent the number of units that flow from node i to node j.)

(a)

Create a spreadsheet model for this problem. What is the optimal solution?

(X₁₃, X₁₄, X₂₃, X₂₄, X₃₄, X₃₅, X₃₆, X₄₃, X₄₆, X₄₇, X₅₆, X₆₇) =

(b)

Suppose that no more than 1,000 units of blood can be transported over any one arc. What is the optimal solution to this revised problem?

(X₁₃, X₁₄, X₂₃, X₂₄, X₃₄, X₃₅, X₃₆, X₄₃, X₄₆, X₄₇, X₅₆, X₆₇) =