Consider the maximum flow problem formulated in Figures 6.7 and 6.8 for the BMZ case study. Redraw Figure 6.7 and insert the optimal shipping quantities (cells D4:D12 in Figure 6.8) in parentheses above the respective arcs. Examine the capacities of these arcs. Explain why these arc capacities ensure that the shipping quantities in parentheses must be an optimal solution because the maximum flow cannot exceed 150.
FIGURE 6.7

FIGURE 6.8

RO [60] NY LA BO ST [70] (70) (50] NO LI (50] loo) (esl [40] [30] [O8] K 1 BMZ Co. Maximum Flow Problem From To Ship Capacity Nodes Net Flow Supply/Demand Stuttgart Stuttgart Stuttgart 4 Rotterdam 50 50 Stuttgart 150 Bordeaux 70 70 Rotterdam 6. Lisbon 30 40 Bordeaux Rotterdam New York 50 60 Lisbon Bordeaux New York 30 40 New York 9. Bordeaux New Orleans 40 50 New Orleans %3D 30 30 Los Angeles -150 10 Lisbon New Orleans 11 New York Los Angeles 80 80 12 New Orleans Los Angeles 70 70 13 14 Maximum Flow 150 VI