Caterer problem

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A caterer has booked his services for the next LaTeX: T days. He requires LaTeX: r_t fresh napkins on the t-th day, LaTeX: t=1,\ldots,T. He sends his soiled napkins to the laundry, which has 3 speeds of service: LaTeX: s=1, 2, or LaTeX: 3 days. The faster the service, the higher the cost, LaTeX: c_s, of laundering a napkin. He can also purchase new napkins at a cost, LaTeX: c_0. With an initial stock of LaTeX: N napkins, the caterer wishes to minimize his total cost. (This can be formulated as a transportation problem.)

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