At a small cellular phone company, servers must spend a half hour discussing options with each possible customer who comes in. During any half hour period, either 0,1 , or 2 customers will come in, with probabilities \(1 / 2,1 / 4\), and \(1 / 4\) respectively. A total of three servers can be summoned to work if necessary. Customers who are being served will not leave before their service is complete. If there are 6 or more customers in the store, including those in service, all of those not currently being served will leave without being served, otherwise if there are 5 or fewer customers in the store all of those who are not being served will stay for the next half hour period. The company can control how many servers are on the floor, but they pay a price of \(s\) dollars per half hour per server to keep them there. They earn a profit of \(p\) dollars for each customer who stays and gets served. The store is open from 9:00 am to 4:00 pm. Customers left over at closing time leave without service or profit to the company. Formulate this problem as a Markov decision problem, describing the state and action spaces, the transition matrices, and the per period and terminal reward functions.