You are helping to manage PharmaGiant's New Jersey manufacturing facility, which chemically synthesizes a wide variety of medications.  Currently, the facility is operating on a regular Monday-Friday schedule, and shuts down on weekends.  One ingredient used in many of the production processes is purified propane.  Over the past 10 weeks, the plant's consumption of this material (in barrels) has been as follows:

You have been asked to plan propane purchasing and inventory for the next two weeks (starting next Monday). 

It is presently the end of Friday, and you have 15 barrels of propane in inventory.  Purified propane costs $50 per barrel, and any orders must be placed at the start of each working day.  You estimate the overhead costs of placing and receive a propane order to be $100.  There is a one-day lead time for orders: orders place at the start of Monday, for example, arrive in time for the start of production on Tuesday.  If you run out of propane inventory during a day of production, you can make up the shortfall by producing it yourself, but that costs $80 per barrel.  You can store up to 30 barrels of propane, and you estimate your inventory holding cost to be $3 per barrel per day, assessed on inventory left over at the end of each day.  If, once any orders arrive, you have more than 30 barrels of propane on hand at the beginning of a day, you must return the excess to your supplier.  However, you do not receive any credit for such returns.

Use forecasting and dynamic programming to arrive at a propane ordering strategy with minimum expected cost.  Value any propane inventory left over at the end of day 10 at $40/barrel.