| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2003 |
| Session | January |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | The Simplex Algorithm |
| Type | Write constraints from tableau |
| Difficulty | Moderate -0.3 This is a standard D1 simplex algorithm question requiring students to read a tableau, write constraints/objective function, then perform the simplex method mechanically. While it has multiple parts and 14 marks total, it follows a completely routine procedure taught explicitly in the specification with no problem-solving insight required—just careful arithmetic and following the pivot rules. It's slightly easier than average A-level questions because it's purely algorithmic execution. |
| Spec | 7.07a Simplex tableau: initial setup in standard format7.07b Simplex iterations: pivot choice and row operations |
| Basic Variable | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | Value |
| \(r\) | 2 | 3 | 4 | 1 | 0 | 8 |
| \(s\) | 3 | 3 | 1 | 0 | 1 | 10 |
| \(P\) | -8 | -9 | -5 | 0 | 0 | 0 |
The tableau below is the initial tableau for a maximising linear programming problem.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Basic Variable & $x$ & $y$ & $z$ & $r$ & $s$ & Value \\
\hline
$r$ & 2 & 3 & 4 & 1 & 0 & 8 \\
$s$ & 3 & 3 & 1 & 0 & 1 & 10 \\
$P$ & -8 & -9 & -5 & 0 & 0 & 0 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item For this problem $x \geq 0$, $y \geq 0$, $z \geq 0$. Write down the other two inequalities and the objective function.
[3]
\item Solve this linear programming problem.
[8]
\item State the final value of $P$, the objective function, and of each of the variables.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2003 Q8 [14]}}