| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2004 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | The Simplex Algorithm |
| Type | Interpret optimal tableau |
| Difficulty | Moderate -0.3 This is a straightforward interpretation question from D1 Simplex Algorithm requiring students to: (a) check optimality by inspecting the profit row for negative values (standard recall), (b) read off basic and non-basic variable values directly from the tableau (routine procedure), and (c) identify the profit coefficient from the objective row. All parts involve direct application of standard simplex tableau reading skills with no problem-solving or novel insight required, making it slightly easier than average. |
| Spec | 7.07a Simplex tableau: initial setup in standard format |
| Basic variable | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | \(t\) | Value |
| \(s\) | 3 | 0 | 2 | 0 | 1 | \(-\frac{2}{3}\) | \(\frac{2}{3}\) |
| \(r\) | 4 | 0 | \(\frac{7}{2}\) | 1 | 0 | 8 | \(\frac{9}{2}\) |
| \(y\) | 5 | 1 | 7 | 0 | 0 | 3 | 7 |
| P | 3 | 0 | 2 | 0 | 0 | 8 | 63 |
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 tableau was obtained.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
Basic variable & $x$ & $y$ & $z$ & $r$ & $s$ & $t$ & Value \\
\hline
$s$ & 3 & 0 & 2 & 0 & 1 & $-\frac{2}{3}$ & $\frac{2}{3}$ \\
\hline
$r$ & 4 & 0 & $\frac{7}{2}$ & 1 & 0 & 8 & $\frac{9}{2}$ \\
\hline
$y$ & 5 & 1 & 7 & 0 & 0 & 3 & 7 \\
\hline
P & 3 & 0 & 2 & 0 & 0 & 8 & 63 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item State, giving your reason, whether this tableau represents the optimal solution. [1]
\item State the values of every variable. [3]
\item Calculate the profit made on each unit of $y$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2004 Q2 [6]}}