| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2009 |
| Session | January |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | The Simplex Algorithm |
| Type | Explain unbounded solution |
| Difficulty | Standard +0.3 This is a standard Simplex algorithm question testing routine procedures: setting up tableaux, identifying pivots, performing iterations, and recognizing unbounded solutions. While it requires multiple steps, each part follows textbook procedures with no novel problem-solving. The unboundedness recognition in (b)(v) is a standard pattern students learn to identify. Slightly easier than average due to its procedural nature. |
| 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 |
I appreciate you sharing this content, but what you've provided appears to be a data table or matrix rather than a mark scheme with marking annotations (M1, A1, B1, DM1, etc).
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1. The actual mark scheme text that contains marking points and annotations
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Once you share the proper mark scheme content with annotations, I'll be happy to clean it up and convert unicode symbols to LaTeX notation.3
\begin{enumerate}[label=(\alph*)]
\item Display the following linear programming problem in a Simplex tableau.
$$\begin{array} { l l }
\text { Maximise } & P = 4 x - 5 y + 6 z \\
\text { subject to } & 6 x + 7 y - 4 z \leqslant 30 \\
& 2 x + 4 y - 5 z \leqslant 8 \\
& x \geqslant 0 , y \geqslant 0 , z \geqslant 0
\end{array}$$
\item The Simplex method is to be used to solve this problem.
\begin{enumerate}[label=(\roman*)]
\item Explain why it is not possible to choose a pivot from the $z$-column initially.
\item Identify the initial pivot and explain why this particular element should be chosen.
\item Perform one iteration using your initial tableau from part (a).
\item State the values of $x , y$ and $z$ after this first iteration.
\item Without performing any further iterations, explain why $P$ has no finite maximum value.
\end{enumerate}\item Using the same inequalities as in part (a), the problem is modified to
$$\text { Maximise } \quad Q = 4 x - 5 y - 20 z$$
\begin{enumerate}[label=(\roman*)]
\item Write down a modified initial tableau and the revised tableau after one iteration.
\item Hence find the maximum value of $Q$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA D2 2009 Q3 [15]}}