I was looking at a problem, and I was wondering how I would set this up. Any help would be welcome. Thank you!

A store stocks a particular item. The demand for the product each day is 1 item with probability 1/6, 2 items with probability 3/6, and 3 items with probability 2/6. Assume that the daily demands are independent and identically distributed. The store uses an (s, S) = (2, 4) policy to manage its inventory: each evening if the remaining stock is less than or equal to s items, the store orders enough to bring the total stock up to S items next morning. These items reach the store before the beginning of the following day. Assume that any demand is lost when the item is out of stock. Assume that each item sells at $150, the variable cost per item is cv = $50, the fixed cost for each order is cf = $100, and the holding cost is $5 for each item held overnight. Find the long-run average profit per day

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    $\begingroup$ We use dollar signs to set off MathJax math formatting on this site. If you want to write 150 dollars, you should write dollar backslash dollar 150 dollar, where the backslash is an escape character to render the following dollar the way you want. $\endgroup$ – Ross Millikan Mar 11 '15 at 2:27

This is a Markov chain. First you want to compute the transition probabilities from today's stock to tomorrow's stock. There are only three states. You can compute the expected profit at each stock level. Now use the equilibrium probability of stock levels to compute the expected profit per day.


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