17. Production planning. DirectCo sells an item whose demand over the next four months is 100, 140, 210 and 180 units, respectively. The company can stock just enough supply to meet each month's demand, or it can overstock to meet the demand for two or more successive and consecutive months. In the latter case, a holding cost of $1.20 is charged per overstocked unit per month. DirectCo estimates the unit purchase prices for the next four months to be $15, $12, $10 and $14, respectively. A setup cost of $200 is incurred each time a purchase order is placed. The company wants to develop a purchasing plan that will minimize the total costs of ordering, purchasing and holding the item in stock. Formulate the problem as a shortest path model