# Caterer problem

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.)