7. Nigel has a business renting out his fleet of bicycles to tourists.
At the start of each year Nigel must decide on one of two actions:
- Keep his fleet of bicycles, incurring maintenance costs.
- Replace his fleet of bicycles.
The cost of keeping the fleet of bicycles, the cost of replacing the fleet of bicycles and the annual income are dependent on the age of the fleet of bicycles.
Table 1 shows these amounts, in \(\pounds 1000\) s.
\begin{table}[h]
| Age of fleet of bicycles | new | 1 year old | 2 years old | 3 years old | 4 years old |
| Cost of keeping (£1000s) | 0 | 1 | 2 | 3 | 8 |
| Cost of replacing (£1000s) | - | 7 | 8 | 9 | 10 |
| Income (£1000s) | 11 | 8 | 5 | 2 | 0 |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
Nigel has a new fleet of bicycles now and wishes to maximise his total profit over the next four years.
He is planning to sell his business at the end of the fourth year.
The amount Nigel will receive will depend on the age of his fleet of bicycles.
These amounts, in £1000s, are shown in Table 2.
\begin{table}[h]
| Age of fleet of bicycles | | at end of 4th year |
| | | | |
| Amount received at end | | of 4th year \(( \pounds 1000 \mathrm {~s} )\) |
| 6 | 4 | 2 | 1 |
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{table}
Complete the table in the answer book to determine Nigel's best strategy to maximise his total profit over the next four years. You must state the action he should take each year (keep or replace) and his total profit.
(Total 13 marks)