Consider an inventory Markov chain model where a maximum of M products can be stored. On day n + 1, a random number D_n of product is demanded, and these orders are fulfilled immediately if enough product is available. If the product is unavailable, the sale is lost; the orders are taken elsewhere to be fulfilled. Reordering decisions are made at the end of the day as follows: If the amount of inventory is below some number s, then the store manager orders enough new product to fill up the storage, so that M products are available the next morning (overnight delivery!). The stochastic update rule for this model is Xn+1={max()MDn,0)max(sDn,0)ifXn<sifsXnM. Describe how you would compute the long-run average number amount of lost sales per day (number of customers who try to buy the product but request it when it is not available). Be as precise as you can, allowing{Dn}n=0 to be independent, identically distributed random variables with arbitrary probability distribution on the nonnegative integers.