Consider an infinite period inventory problem, where at the beginning of each period, a decision must be made about how many items to produce. Assume that the production time is negligible. The setup cost is $10 and unit production cost is $5. The unit holding cost for the item is $4. You can assume that the holding cost is incurred the entire period as we did in class. Suppose that at most 2 items can be stored. The demand during each period is either 0, or 1, or 2 with equal probability. If the demand exceeds the suppy available during the period, then those sales are lost and a shortage cost is incurred, namely, $8 for a shortage of 1 unit and $32 for a shortage of 2 units. Compute the long-run average cost under the policy where the production always produces up to 2 units.