| Exam Board | Edexcel |
|---|---|
| Module | FD2 (Further Decision 2) |
| Year | 2020 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Dynamic programming resource allocation |
| Difficulty | Standard +0.3 This is a standard textbook dynamic programming problem requiring systematic table completion using the recurrence relation. While it involves multiple stages and careful bookkeeping, it follows a completely algorithmic procedure with no novel insight required—students simply apply the learned DP algorithm mechanically to maximize profit across 5 batches. |
| 1 | 2 | 3 | 4 | |
| A | ||||
| B | ||||
| C | ||||
| D |
| 1 | 2 | 3 | 4 | |
| A | ||||
| B | ||||
| C | ||||
| D |
| 1 | 2 | 3 | 4 | |
| A | ||||
| B | ||||
| C | ||||
| D |
| 1 | 2 | 3 | 4 | |
| A | ||||
| B | ||||
| C | ||||
| D |
| 1 | 2 | 3 | 4 | |
| A | ||||
| B | ||||
| C | ||||
| D |
| 1 | 2 | 3 | 4 | |
| A | ||||
| B | ||||
| C | ||||
| D |
| 1 | 2 | 3 | 4 | |
| A | ||||
| B | ||||
| C | ||||
| D |
| 1 | 2 | 3 | 4 | |
| A | ||||
| B | ||||
| C | ||||
| D |
| P | Q | R | Supply | |
| A | 25 | 24 | 17 | 42 |
| B | 7 | 12 | 14 | 68 |
| C | 13 | 11 | 20 | 25 |
| D | 16 | 15 | 13 | 40 |
| Demand | 59 | 72 | 44 |
| P | Q | R | |
| A | |||
| B | |||
| C | |||
| D |
| P | Q | R | |
| A | |||
| B | |||
| C | |||
| D |
| P | Q | R | |
| A | |||
| B | |||
| C | |||
| D |
| P | Q | R | |
| A | |||
| B | |||
| C | |||
| D |
| P | Q | R | |
| A | |||
| B | |||
| C | |||
| D |
| P | Q | R | |
| A | |||
| B | |||
| C | |||
| D |
| P | Q | R | |
| A | |||
| B | |||
| C | |||
| D |
| P | Q | R | |
| A | |||
| B | |||
| C | |||
| D |
| P | Q | R | |
| A | |||
| B | |||
| C | |||
| D |
| \cline { 2 - 4 } \multicolumn{1}{c|}{} | Option X | Option Y | Option Z |
| Option Q | 1 | 5 | 3 |
| Option R | 4 | - 3 | 1 |
| Option S | 2 | - 4 | - 2 |
| Option T | 3 | - 2 | 0 |
| Stage | State | Action | Destination | Value |
| Trainers | 0 | 0 | 0 | 0 |
| Stage | State | Action | Destination | Value |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Trainers stage: states \(0\)–\(5\), values \(0, 50, 90, 170, 225, 295\) | B1 | CAO for first stage (all six rows); candidates may start with state 5 |
| Sandals stage states \(1, 2, 3\): correct value column entries e.g. \(70, 120, 170\) (starred values) | M1, A1, A1 | At least 9 rows in first half of second stage; value column complete with at least one value correct per state; CAO for states \(0,1,2,3\) |
| Sandals stage states \(4, 5\): correct value column entries e.g. \(245, 300\) (starred values) | M1, A1, A1 | At least 11 rows in second half; value column complete; CAO for states \(4\) and \(5\) |
| High heels stage: \(305, 305, x+120, 285, 320, 300\) | M1, A1ft | At least 6 rows; value column complete with at least 3 values correct |
| \(320\) and \(x + 120\) | A1ft | Must have earned all previous M marks; ft their result |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Trainers: 0, Sandals: 4, High heels: 1 | B1 | One correct allocation (dependent on first three M marks in (a)) |
| Trainers: 1, Sandals: 1, High heels: 3 | B1 | Both correct (dependent on first three M marks in (a)) |
# Question 7:
## Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Trainers stage: states $0$–$5$, values $0, 50, 90, 170, 225, 295$ | B1 | CAO for first stage (all six rows); candidates may start with state 5 |
| Sandals stage states $1, 2, 3$: correct value column entries e.g. $70, 120, 170$ (starred values) | M1, A1, A1 | At least 9 rows in first half of second stage; value column complete with at least one value correct per state; CAO for states $0,1,2,3$ |
| Sandals stage states $4, 5$: correct value column entries e.g. $245, 300$ (starred values) | M1, A1, A1 | At least 11 rows in second half; value column complete; CAO for states $4$ and $5$ |
| High heels stage: $305, 305, x+120, 285, 320, 300$ | M1, A1ft | At least 6 rows; value column complete with at least 3 values correct |
| $320$ and $x + 120$ | A1ft | Must have earned all previous M marks; ft their result |
## Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| Trainers: 0, Sandals: 4, High heels: 1 | B1 | One correct allocation (dependent on first three M marks in (a)) |
| Trainers: 1, Sandals: 1, High heels: 3 | B1 | Both correct (dependent on first three M marks in (a)) |7. A manufacturer can export five batches of footwear each year. Each exported batch contains just one type of footwear. The types of footwear are trainers, sandals or high heels.
The table below shows the profit, in $\pounds 1000$ s, for the number of batches of each type of footwear.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
& 1 & 2 & 3 & 4 \\
\hline
A & & & & \\
\hline
B & & & & \\
\hline
C & & & & \\
\hline
D & & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
& 1 & 2 & 3 & 4 \\
\hline
A & & & & \\
\hline
B & & & & \\
\hline
C & & & & \\
\hline
D & & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
& 1 & 2 & 3 & 4 \\
\hline
A & & & & \\
\hline
B & & & & \\
\hline
C & & & & \\
\hline
D & & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | l | l | l | l | l | }
\hline
& 1 & 2 & 3 & 4 \\
\hline
A & & & & \\
\hline
B & & & & \\
\hline
C & & & & \\
\hline
D & & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | l | l | l | l | l | }
\hline
& 1 & 2 & 3 & 4 \\
\hline
A & & & & \\
\hline
B & & & & \\
\hline
C & & & & \\
\hline
D & & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | l | l | l | l | l | }
\hline
& 1 & 2 & 3 & 4 \\
\hline
A & & & & \\
\hline
B & & & & \\
\hline
C & & & & \\
\hline
D & & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | l | l | l | l | l | }
\hline
& 1 & 2 & 3 & 4 \\
\hline
A & & & & \\
\hline
B & & & & \\
\hline
C & & & & \\
\hline
D & & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
& 1 & 2 & 3 & 4 \\
\hline
A & & & & \\
\hline
B & & & & \\
\hline
C & & & & \\
\hline
D & & & & \\
\hline
\end{tabular}
\end{center}
2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e0fc09f9-06ea-4528-a2de-f409112d85cc-12_956_1333_258_283}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e0fc09f9-06ea-4528-a2de-f409112d85cc-13_954_1322_260_278}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
3.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
& P & Q & R & Supply \\
\hline
A & 25 & 24 & 17 & 42 \\
\hline
B & 7 & 12 & 14 & 68 \\
\hline
C & 13 & 11 & 20 & 25 \\
\hline
D & 16 & 15 & 13 & 40 \\
\hline
Demand & 59 & 72 & 44 & \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{center}
\end{table}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& P & Q & R \\
\hline
A & & & \\
\hline
B & & & \\
\hline
C & & & \\
\hline
D & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& P & Q & R \\
\hline
A & & & \\
\hline
B & & & \\
\hline
C & & & \\
\hline
D & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& P & Q & R \\
\hline
A & & & \\
\hline
B & & & \\
\hline
C & & & \\
\hline
D & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& P & Q & R \\
\hline
A & & & \\
\hline
B & & & \\
\hline
C & & & \\
\hline
D & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& P & Q & R \\
\hline
A & & & \\
\hline
B & & & \\
\hline
C & & & \\
\hline
D & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& P & Q & R \\
\hline
A & & & \\
\hline
B & & & \\
\hline
C & & & \\
\hline
D & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& P & Q & R \\
\hline
A & & & \\
\hline
B & & & \\
\hline
C & & & \\
\hline
D & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& P & Q & R \\
\hline
A & & & \\
\hline
B & & & \\
\hline
C & & & \\
\hline
D & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& P & Q & R \\
\hline
A & & & \\
\hline
B & & & \\
\hline
C & & & \\
\hline
D & & & \\
\hline
\end{tabular}
\end{center}
4.
.\\
5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e0fc09f9-06ea-4528-a2de-f409112d85cc-21_666_1239_1155_413}
\captionsetup{labelformat=empty}
\caption{Diagram 1}
\end{center}
\end{figure}
6.
Player A
\begin{table}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Player B}
\begin{tabular}{ | l | c | c | c | }
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & Option X & Option Y & Option Z \\
\hline
Option Q & 1 & 5 & 3 \\
\hline
Option R & 4 & - 3 & 1 \\
\hline
Option S & 2 & - 4 & - 2 \\
\hline
Option T & 3 & - 2 & 0 \\
\hline
\end{tabular}
\end{center}
\end{table}
7.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
Stage & State & Action & Destination & Value \\
\hline
Trainers & 0 & 0 & 0 & 0 \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
Stage & State & Action & Destination & Value \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
& & & & \\
\hline
\end{tabular}
\end{center}
\hfill \mbox{\textit{Edexcel FD2 2020 Q7 [12]}}