\(A, B, C, D, E, F, G\)

The products at a particular factory are manufactured in phases. The same equipment is utilized for each phase, but it must be formatted differently to accomplish different tasks. The transition time to convert between a format for one task and another task varies. The times are given in Table 12.13. In the following exercises, use the table and the nearest neighbor method to find an order in which to complete the tasks, which keeps the transition times down and ends with the same set up as it began so that the factory is ready to start the next batch. Assume that there are no restrictions on which tasks can be completed in which order. Hint: The nearest neighbor algorithm may give a different result depending on which vertex is the starting vertex, so, you must check all possibilities.

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Task A B C D E F G A 0 75 130 45 120 70 100 B 75 75 0 140 55 65 115 25 60 60 C 130 140 0 35 55 20 125 D 45 65 35 0 50 30 40 E 120 20 115 55 50 50 0 95 145 F 70 25 20 30 95 0 15 G 100 60 60 125 40 145 15 15 0 Manufacturing Equipment Transition Times in Minutes