This question is operations research which can be found in 'Operations Research An Introduction by Hamdy A. Taha (z-lib.org)' textbook. Please use provide AMPL code as well.

Exercise (Exercise 6-15): Production Planning. DirectCo sells an item whose demands over the next 4 months are 100,140,210, and 180, respectively. The company can stock just enough supply to meet each month's demand, or it can overstoch to meet the demand for two or more 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 4 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 using the linear programming formulation of the shortest path model and solve it using AMPL to obtain the optimum solution