2. An engineering firm makes motors. They can make up to five in any one month, but if they make more than four they have to hire additional premises at a cost of \(\pounds 500\) per month. They can store up to two motors for \(\pounds 100\) per motor per month. The overhead costs are \(\pounds 200\) in any month in which work is done.
Motors are delivered to buyers at the end of each month. There are no motors in stock at the beginning of May and there should be none in stock after the September delivery.
The order book for motors is:
| Month | May | June | July | August | September |
| Number of motors | 3 | 3 | 7 | 5 | 4 |
Use dynamic programming to determine the production schedule that minimises the costs, showing your working in the table provided below.
| Stage (month) | State (Number in store at start of month) | Action (Number made in month) | Destinatio n (Number in store at end of month) | Value (cost) |
| | | | |
\section*{Production schedule}
| Month | May | June | July | August | September |
| | | | | |
Total cost: \(\_\_\_\_\)