The Pigskin company will produce footballs over the next six months. Forecasted demand and production costs over this time period are:
| Month | 1 | 2 | 3 | 4 | 5 | 6 |
| Demand (Cases of 100) |
100 | 150 | 300 | 350 | 250 | 100 |
| Unit Production Cost | $ 12.50 | $ 12.55 | $ 12.70 | $ 12.80 | $ 12.85 | $ 12.95 |
Pigskin has a monthly production capacity of 300 cases. They currently has 50 cases of footballs in inventory, and has enough capacity to store up to 100 cases. The holding cost of keeping a football in inventory for a month is estimated to be 5% of the cost of producing in that month.
Pigskin has decided that they want to meet the entire demand for footballs over the 6-month period. How can they do that at minimum cost?