A company receives the customer orders of a product for the next four months, 80, 65, 100, and 70 units respectively (no backlogging is allowed). Suppose that for the production in each month, a fixed set up cost $150 is incurred. The production cost is $5 per unit during these months. The storage cost from one month to the next is $2 per unit (based on the inventory at the end of that month). Formulate a shortest path problem for the above problem and solve it to find a production schedule for the company that meets the demands of the next four months with the minimal production cost.