| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Dynamic programming production scheduling |
| Difficulty | Challenging +1.8 This is a multi-stage decision problem requiring systematic dynamic programming with multiple constraints (production capacity, storage limits, hiring costs, overhead). Students must construct a complete DP table working backwards through 5 months, tracking states and costs carefully. While the technique is standard for D2, the problem requires sustained accuracy over many calculations and careful consideration of feasibility constraints, making it significantly harder than routine exercises. |
| Spec | 7.07a Simplex tableau: initial setup in standard format7.07b Simplex iterations: pivot choice and row operations7.07c Interpret simplex: values of variables, slack, and objective7.07d Simplex terminology: basic feasible solution, basic/non-basic variable7.07e Graphical interpretation: iterations as edges of convex polygon7.07f Algebraic interpretation: explain simplex calculations |
| Month | January | February | March | April | May |
| Number of robots required | 3 | 2 | 2 | 5 | 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| May stage values computed (e.g. state 0: \(+300=800^*\), state 1: \(+100=600^*\), etc.) | M1 A1(2) | |
| April stage values computed | M1, A1, A1(3) | |
| March stage values computed | M1, A1, A1, A1(4) | |
| February stage values computed | M1, A1, A1(3) | |
| January stage values computed | (included above) | |
| Optimal policy: Jan\(=3\), Feb\(=3\), March\(=3\), April\(=3\), May\(=4\) | M1, A1(2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Cost £31.00 |
## Question 7:
| Answer/Working | Marks | Guidance |
|---|---|---|
| May stage values computed (e.g. state 0: $+300=800^*$, state 1: $+100=600^*$, etc.) | M1 A1(2) | |
| April stage values computed | M1, A1, A1(3) | |
| March stage values computed | M1, A1, A1, A1(4) | |
| February stage values computed | M1, A1, A1(3) | |
| January stage values computed | (included above) | |
| Optimal policy: Jan$=3$, Feb$=3$, March$=3$, April$=3$, May$=4$ | M1, A1(2) | |
Based on the image provided, the content is very minimal. Here is what can be extracted:
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**Question (number not visible):**
| Answer/Working | Marks | Guidance |
|---|---|---|
| Cost £31.00 | | |
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*Note: The question number, mark allocation codes (M1/A1/B1 etc.), and any additional guidance notes are not visible in this page of the mark scheme. This appears to be only a partial page (page 7) of the GCE Further Pure Mathematics and Decision Mathematics mock paper mark schemes (UA019582).*7. D2 make industrial robots. They can make up to four in any one month, but if they make more than three they need to hire additional labour at a cost of $\pounds 300$ per month. They can store up to three robots at a cost of $\pounds 100$ per robot per month. The overhead costs are $\pounds 500$ in any month in which work is done.
The robots are delivered to buyers at the end of each month. There are no robots in stock at the beginning of January and there should be none in stock at the end of May.
The order book for January to May is:
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Month & January & February & March & April & May \\
\hline
Number of robots required & 3 & 2 & 2 & 5 & 4 \\
\hline
\end{tabular}
\end{center}
Use dynamic programming to determine the production schedule that minimises the costs, showing your working in the table provided in the answer book. State the minimum cost.\\
(Total 14 marks)\\
\hfill \mbox{\textit{Edexcel D2 Q7 [14]}}