Consider an infinite-period inventory problem involving a single product where, at the begininning of each period, a decision must be made about how many items to produce during that period. The set up cost is $10, and unit production cost is $5. The holding cost for each item not sold during the period is $4 ( a max of two items can be stored). The demand during each period has a known probability distribution, namely, a probability of 1/3 of 0, 1, and 2 items, respectively. If the demand exceeds the supply avainlable during the period, then those sales are lost and a shortage cost (including lost revenue) is incurred, namely, $8 and $32, for a shortage of 1 and 2 items respectively.

Formulate a linear programming model for finding an optimal policy