D2 June 2013 Q7

EdexcelOld spec13 marksDynamic Programming

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 £1000s.

Age of fleet of bicyclesnew1 year old2 years old3 years old4 years old
Cost of keeping (£1000s)01238
Cost of replacing (£1000s)–78910
Income (£1000s)118520

Table 1

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.

Age of fleet of bicycles at end of 4th year1 year old2 years old3 years old4 years old
Amount received at end of 4th year (£1000s)6421

Table 2

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. (13)

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