| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | The Simplex Algorithm |
| Type | Perform one Simplex iteration |
| Difficulty | Moderate -0.8 This is a routine mechanical application of the Simplex algorithm requiring identification of pivot column (most negative in profit row), pivot row (minimum ratio test), and performing elementary row operations. It's a standard textbook exercise testing procedural fluency rather than problem-solving or insight, making it easier than average A-level maths questions. |
| 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 objective |
| Basic variable | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | Value |
| \(r\) | 2 | 0 | 4 | 1 | 0 | 80 |
| \(s\) | 1 | 4 | 2 | 0 | 1 | 160 |
| \(P\) | - 2 | - 8 | - 20 | 0 | 0 | 0 |
2. A three-variable linear programming problem in $x , y$ and $z$ is to be solved. The objective is to maximise the profit $P$. The following initial tableau was obtained.
\begin{center}
\begin{tabular}{ | c | r | r | r | r | r | r | }
\hline
Basic variable & \multicolumn{1}{|c|}{$x$} & \multicolumn{1}{c|}{$y$} & \multicolumn{1}{c|}{$z$} & $r$ & \multicolumn{1}{c|}{$s$} & Value \\
\hline
$r$ & 2 & 0 & 4 & 1 & 0 & 80 \\
\hline
$s$ & 1 & 4 & 2 & 0 & 1 & 160 \\
\hline
$P$ & - 2 & - 8 & - 20 & 0 & 0 & 0 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Taking the most negative number in the profit row to indicate the pivot column, perform one complete iteration of the simplex algorithm, to obtain tableau $T$. State the row operations that you use.
\item Write down the profit equation shown in tableau $T$.
\item State whether tableau $T$ is optimal. Give a reason for your answer.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q2 [7]}}