Suppose now that the three locations (Memphis, Philadelphia, Toledo) are potential locations, i.e., each plant would only be constructed if it improves overall cost (i.e., transportation plus plant fixed costs). The data is repeated here with the (annualized) plant fixed costs shown additionally.

What changes would you make to the model in part (a) so that we can determine the optimal locations of the plants as well as the optimal demand allocation (i.e. minimize both transportation as well as fixed costs).

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Plant Location Distribution Center Plant Annualized Fixed Costs Atlanta Boston Chicago Capacity $3 5 $50,000 Memphis 30,000 2 Philadelphia 4 35,000 35,000 45,000 48,000 Toledo