Consider the manufacturing line of Example 12.10, where the optimal numbers of machines in...

Consider the manufacturing line of Example 12.10, where the optimal numbers of machines in workstations 1 through 4 turned out to be 3, 3, 2, and 2, respectively.

(a) Why do you think that it is optimal to have 3 rather than 2 machines in station 2?

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(b) Given that there should be 3 machines in station 2, why should there not be 3 machines in station 3?

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(c) Given that there should be 3 machines in station 2, why should there not be 2 machines in station 1? (If there were 2 and 3 machines in stations 1 and 2, respectively, then both stations would have the same potential processing rate of 6 per hour.)

Example 12.10

FIGURE 12.24 Layout for the manufacturing line.

TABLE 12.27 Mean processing time for a machine at each of the four stations, manufacturing line

FIGURE 12.25 Maximum average profit at configuration i, M_i, for the manufacturing line.