7. A company assembles microlight aircraft.
They can assemble up to four aircraft in any one month, but if they assemble more than three they will have to hire additional space at a cost of \(\pounds 1000\) per month.
They can store up to two aircraft at a cost of \(\pounds 500\) each per month.
The overhead costs are \(\pounds 2000\) in any month in which work is done.
Aircraft are delivered at the end of each month. There are no aircraft in stock at the beginning of March and there should be none in stock at the end of July.
The order book for aircraft is
| Month | March | April | May | June | July |
| Number ordered | 3 | 4 | 2 | 4 | 3 |
Use dynamic programming to determine the production schedule which minimises the costs. Show your working in the table provided in the answer book and state the minimum production cost.
(Total 14 marks)