7. Remy builds canoes.
He can build up to five canoes each month, but if he wishes to build more than three canoes in any one month he has to hire an additional worker at a cost of \(\pounds 400\) for that month.
In any month when canoes are built, the overhead costs are \(\pounds 150\)
A maximum of three canoes can be held in stock in any one month, at a cost of \(\pounds 25\) per canoe per month.
Canoes must be delivered at the end of the month.
The order book for canoes is
| Month | January | February | March | April | May |
| Number ordered | 2 | 2 | 5 | 6 | 4 |
There is no stock at the beginning of January and Remy plans to have no stock after the May delivery.
- Use dynamic programming to determine the production schedule that minimises the costs given above. Show your working in the table provided in the answer book and state the minimum cost.
(13)
The cost of materials is \(\pounds 200\) per canoe and the cost of Remy’s time is \(\pounds 450\) per month. Remy sells the canoes for \(\pounds 700\) each. - Determine Remy's total profit for the five-month period.
(2)
(Total 15 marks)