| Exam Board | Edexcel |
|---|---|
| Module | FD2 (Further Decision 2) |
| Session | Specimen |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Dynamic programming production scheduling |
| Difficulty | Challenging +1.2 This is a standard dynamic programming problem with clearly defined states, transitions, and costs. While it requires systematic working through multiple stages and careful bookkeeping of feasible states, the problem structure is straightforward with no novel insights needed. The constraints are explicit and the table format guides students through the solution method, making it moderately harder than average but well within typical FP2/FD2 scope. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
| Month | January | February | March | April | May |
| Number ordered | 3 | 2 | 6 | 3 | 4 |
7. A company assembles boats.
They can assemble up to five boats in any one month, but if they assemble more than three they will have to hire additional space at a cost of $\pounds 800$ per month.
The company can store up to two boats at a cost of $\pounds 350$ each per month.\\
The overhead costs are $\pounds 1500$ in any month in which work is done.\\
Boats are delivered at the end of each month. There are no boats in stock at the beginning of January and there must be none in stock at the end of May.
The order book for boats is
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
Month & January & February & March & April & May \\
\hline
Number ordered & 3 & 2 & 6 & 3 & 4 \\
\hline
\end{tabular}
\end{center}
Use dynamic programming to determine the production schedule which minimises the costs to the company. Show your working in the table provided in the answer book and state the minimum production cost.
\hfill \mbox{\textit{Edexcel FD2 Q7 [12]}}