Question
Suppose youre running a lightweight consulting businessjust you, two associates, and some rented equipment. Your clients are distributed between the East Coast and the West
Suppose youre running a lightweight consulting businessjust you, two associates, and some rented equipment. Your clients are distributed between the East Coast and the West Coast, and this leads to the following question. Each month, you can either run your business from an office in New York (NY) or from an office in San Francisco (SF). In month i, youll incur an operating cost of Ni if you run the business out of NY; youll incur an operating cost of Si if you run the business out of SF. It depends on the distribution of client demands for that month. However, if you run the business out of one city in month i, and then out of the other city in month i + 1, then you incur a fixed moving cost of M to switch base offices. Given a sequence of n months, a plan is a sequence of n locations each one equal to either NY or SFsuch that the i th location indicates the city in which you will be based in the i th month. The cost of a plan is the sum of the operating costs for each of the n months, plus a moving cost of M for each time you switch cities. The plan can begin in either city. The problem: Given a value for the moving cost M, and sequences of operating costs {N1, . . . , Nn} and {S1, . . . , Sn}.
Give a recurrence relation, tabular computation and trace back procedure for this problem.
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