7. D2 make industrial robots. They can make up to four in any one month, but if they make more than three they need to hire additional labour at a cost of \(\pounds 300\) per month. They can store up to three robots at a cost of \(\pounds 100\) per robot per month. The overhead costs are \(\pounds 500\) in any month in which work is done.
The robots are delivered to buyers at the end of each month. There are no robots in stock at the beginning of January and there should be none in stock at the end of May.
The order book for January to May is:
| Month | January | February | March | April | May |
| Number of robots required | 3 | 2 | 2 | 5 | 4 |
Use dynamic programming to determine the production schedule that minimises the costs, showing your working in the table provided in the answer book. State the minimum cost.
(Total 14 marks)