Boralis manufacture backpacks for serious hikers. The demand for its product occurs during March to June of each year. Boralis estimates the demand for the four months to be 100, 200, 180, and 300 units, respectively. The company uses part-time labor to manufacture the backpacks and, accordingly, its production capacity varies monthly. It is estimated that Boralis can produce 50, 150, 280, and 270 units in March through June. A current month's demand may be satisfied in one of three ways:
1. Current month's production.
2. Surplus production in an earlier month.
3. Surplus production in a later month (backordering).
In the first case, the production cost per backpack is $40. The second case incurs an additional holding cost of $.50 per back-pack per month. In the third case, an additional penalty cost of $2.00 per backpack is incurred for each month delay. Boralis wishes to determine the optimal production schedule for the four months.