A2 June 2025 Q5

EdexcelCurrent spec13 marksDynamic Programming

5. Anvi makes boats during the winter months. She can make up to five boats each month.

If she builds more than three boats in any one month, she must hire an assistant at a cost of £400 for that month.

In any month in which boats are made, the overhead costs are £60 for each boat made that month.

A maximum of three boats can be held in storage at the end of each month, at a cost of £70 per boat per month.

Boats must be delivered at the end of each month.

The order schedule for boats is

MonthNovemberDecemberJanuaryFebruaryMarch
Number ordered25643

There are no boats in storage at the beginning of November.
Anvi plans to have no boats left in storage after the end of the March delivery.

(a) Use dynamic programming to determine the production schedule that minimises the costs given above. Complete the working in the table provided in the answer book and state the minimum cost. (12)

[The table in the answer book begins as follows.]

StageStateActionDestinationValue
March300210 = 210*
210140 + 60 = 200*
12070 + 120 = 190*
030180 = 180*

The assistant asks to work in November, and Anvi agrees.

(b) Given that more than three boats are now made in November, state the minimum additional cost of producing all the required boats to the schedule shown above. (1)
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