3 Assume that during minute t (the current minute is minute 1), the following sequence of events occurs: (1) At the beginning of the minute, xt customers arrive at the cash register; (2) the store manager decides how many cash registers should be operated during the current minute;

(3) if s cash registers are operated and i customers are present (including the current minute’s arrivals), c(s, i)

customers complete service; and (4) the next minute begins.

A cost of 10¢ is assessed for each minute a customer spends waiting to check out (this time includes checkout time). Assume that it costs c(s) cents to operate s cash registers for 1 minute. Formulate a dynamic programming recursion that minimizes the sum of holding and service costs during the next 60 minutes. Assume that before the first minute’s arrivals, no customers are present and that holding cost is assessed at the end of each minute.