A company receives the customer orders of a product for the next four months, 80, 65, 100, and 70 units respectively (no

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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.