A knife maker must decide each week how many chef knives to make during the week to sell at Saturday’s farmer’s market. Each knife can be sold for 250$. He prefers to not store more than 5 chef knives at his shop at any point in time. Each week, there is a 50% chance one customer wants to buy a chef knife, a 20% chance he sees a demand of 2 chef knives, 15% chance he sees a demand of 3 chef knives, and 15% chance no customers are interested in buying knives.
If he has no knives with him when a customer comes on Saturday, the customer leaves without buying a knife. On those weeks that he chooses to make knives, the knife maker must set up special equipment that costs 300$ per week to run. In addition, it costs him 100$ to make each knife. Knives not sold at the end of the year can be sold one-bay for 50$. Formulate this problem as a Markov decision process, in which the objective is to maximize the total expected income over the next 2 weeks (assuming there are only 2 weeks left this year). Clearly indicate the 5 basic components of this MDP.
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