| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2002 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | The Simplex Algorithm |
| Type | Interpret optimal tableau |
| Difficulty | Moderate -0.8 This is a straightforward interpretation question requiring students to read an optimal simplex tableau and apply standard D1 rules: (a) check non-negative entries in objective row, (b) read off basic variables from the Value column, (c) write the profit equation. No actual simplex iterations or problem-solving required—pure recall and mechanical reading of a given tableau. |
| Spec | 7.07b Simplex iterations: pivot choice and row operations7.07c Interpret simplex: values of variables, slack, and objective |
| Basic variable | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | \(t\) | Value |
| \(r\) | 0 | 0 | \(1 \frac { 2 } { 3 }\) | 1 | 0 | \(- \frac { 1 } { 6 }\) | \(\frac { 2 } { 3 }\) |
| \(y\) | 0 | 1 | \(3 \frac { 1 } { 3 }\) | 0 | 1 | \(- \frac { 1 } { 3 }\) | \(\frac { 1 } { 3 }\) |
| \(x\) | 1 | 0 | -3 | 0 | -1 | \(\frac { 1 } { 2 }\) | 1 |
| \(P\) | 0 | 0 | 1 | 0 | 1 | 1 | 11 |
Total: 10 marks
Question 2:
M1 for attempting to find a common denominator or multiply through by denominators
A1 for correct simplification to a standard form equation
M1 for correct method to solve the resulting equation
A1 for correct solutions
B1 for identifying valid solutions (checking domain restrictions)
DM1 for demonstrating clear algebraic manipulation throughout
Total: 10 marks2. While solving a maximizing linear programming problem, the following tableau was obtained.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
Basic variable & $x$ & $y$ & $z$ & $r$ & $s$ & $t$ & Value \\
\hline
$r$ & 0 & 0 & $1 \frac { 2 } { 3 }$ & 1 & 0 & $- \frac { 1 } { 6 }$ & $\frac { 2 } { 3 }$ \\
\hline
$y$ & 0 & 1 & $3 \frac { 1 } { 3 }$ & 0 & 1 & $- \frac { 1 } { 3 }$ & $\frac { 1 } { 3 }$ \\
\hline
$x$ & 1 & 0 & -3 & 0 & -1 & $\frac { 1 } { 2 }$ & 1 \\
\hline
$P$ & 0 & 0 & 1 & 0 & 1 & 1 & 11 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Explain why this is an optimal tableau.
\item Write down the optimal solution of this problem, stating the value of every variable.
\item Write down the profit equation from the tableau. Use it to explain why changing the value of any of the non-basic variables will decrease the value of $P$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2002 Q2 [6]}}