During the next four months, a customer requires, respectively, 500, 650, 1000, and 700 units of a commodity, and no backlogging is allowed (that is, the customer’s requirements must be met on time). Production costs are $150, $180, $140, and $170 per unit during these months. The storage cost from one month to the next is $20 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 can be sold for $200. Assume there are 10 units of beginning inventory.

Determine how to minimize the net cost incurred in meeting the demands for the next four months. (Write your notation, LP formulation explicitly, submit your managerial reports with computer models, solutions, answer and sensitivity reports attached.)

If the production costs are all set to $150, would your solution change?