Please solve the following Continuous Time Markov Problem:

4. (15 points total) An in-town small-package delivery-service company receives orders for all types delivery services during the work day at a rate of 10 orders per hour. Some medical products require special containers and these special containers need special preparation. For example, small coolers must be sterilized and tted with dry ice, for some blood, blood-plasma or vaccination seruins. The company has instituted a policy of trying to keep ahead of these delivery orders during business day by maintaining an inventory of already-prepared special containers, even though doing so costs money. In fact, 20% of the orders they get do require these specially prepared special containers. Each special container is prepared one-at-a-time, and no order is for more than one product that requires a special container. There is only one technician who is trained to prepare these special containers. The time to prepare a special container is a negative exponential random variable with a mean of 15 minutes. The company's policy is to start the work day with 4 special containers on hand, to use them up as needed, and to replace them as best they can to keep the inventory close to, but not more than 4. In other words, they will start preparing another special container if they have less than 4 on hand, but not otherwise. (a) (5 points) Construct a model to answer this and following questions. State your time units, define your states, and show the transition diagram and transition matrix