KS brand tires11 are shaped in changeable molds type i = 1,

c, m, installed in the company’s 40 presses. Production plans dictate the minimum ri, t and maximum ri, t numbers of molds i that should be operational during time period t = 1,

c, n, and the planning period begins t = 0 with numbers of molds bi installed 1aibi = 402.

There is an adequate supply of molds, but changeovers from one mold to another are expensive, costing an amount ci depending on the mold installed. All 40 presses should be in use in each time period. Demonstrate that the problem of finding a minimum total changeover cost mold schedule can be modeled as a network flow on a suitable time- expanded network by sketching the graph for a case with m = 2 and n = 3, and showing all nodes, arcs, costs, bounds, and node net demands. Some arcs will have nonzero lower bounds. (Hint: Also include supernodes balancing the total number of molds removed and inserted in each time period.)