8. A company makes industrial robots.
They can make up to four robots in any one month, but if they make more than three they will have to hire additional labour at a cost of \(\pounds 400\) per month.
They can store up to two robots at a cost of \(\pounds 150\) per robot per month.
The overhead costs are \(\pounds 300\) in any month in which work is done.
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 after the April delivery.
The order book for robots is
| Month | January | February | March | April |
| Number of robots required | 2 | 2 | 3 | 4 |
Use dynamic programming to determine the production schedule which minimises the costs, showing your working in the table provided in the answer book.
(Total 12 marks)