6 A company produces a product at two plants, 1 and 2.

The unit production cost and production capacity during each period are given in Table 41. The product is instantaneously shipped to the company’s only customer according to the unit shipping costs given in Table 42. If a unit is produced and shipped during period 1, it can still be used to meet a period 2 demand, but a holding cost of $13 per unit in inventory is assessed. At the end of period 1, at most six units may be held in inventory. Demands are as follows: period 1, 9; period 2, 11. Formulate an MCNFP that can be used to minimize the cost of meeting all demands on time. Draw the network and determine the net outflow at each node, the arc capacities, and shipping costs.

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TABLE 41 Unit Production Cost ($) Capacity Plant 1 (period 1) 33 7 Plant 1 (period 2) 43 Plant 2 (period 1) 30 Plant 2 (period 2) 41 469 TABLE 42 Period 1 Period 2 Plant 1 to customer $51 $60 Plant 2 to customer $42 $71