Assignment:
The owner of a furniture store must decide how many recliners to get each month to sell at her store. Each recliner can be sold for $600. She prefers not to store more than 6 recliners at her shop at any point in time. Each month, there is a 45% chance one customer wants to buy a recliner, a 15% chance she sees a demand of 2 recliners, 10% chance she sees a demand of 3 recliners, and 30% chance no customers are interested in buying her recliners. She never sees a demand of more than 3 recliners in any given month. If she has no recliners when a customer comes, the customer leaves without buying a recliner. On those months that she chooses to aquire recliners, she must pay a total fixed cost of $800 for shipping and handling of all recliners. In addition, it costs her $200 to purchase each recliner. Recliners not sold at the end of the year can be sold on e-bay for S300. Formulate this problem as a Markov decision process, in which the objective is to maximize the total expected income over the next 2 months (assuming there are only 2 months left this year). Clearly indicate the 5 basic components of this MDP.