| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 4 |
| 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 values directly from an optimal simplex tableau (basic variables = 0, read values from right column) and write the profit equation from the bottom row. It tests only recall and basic tableau interpretation with no problem-solving, pivoting, or setup required. |
| Spec | 7.07c Interpret simplex: values of variables, slack, and objective7.07d Simplex terminology: basic feasible solution, basic/non-basic variable |
| Basic Variable | x | y | z | r | s | t | value |
| z | \(\frac { 1 } { 4 }\) | \(- \frac { 1 } { 4 }\) | 1 | \(\frac { 1 } { 4 }\) | 0 | 0 | 2 |
| s | \(\frac { 5 } { 4 }\) | \(\frac { 7 } { 4 }\) | 0 | \(- \frac { 3 } { 4 }\) | 1 | 0 | 4 |
| t | 3 | \(\frac { 5 } { 2 }\) | 0 | \(- \frac { 1 } { 2 }\) | 0 | 1 | 2 |
| P | -2 | -4 | 0 | \(\frac { 5 } { 4 }\) | 0 | 0 | 10 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | \(x = 0, y = 0, z = 2\) | B2, 1, 0 (2) |
| (b) | \(P - 2x - 4y + \frac{5}{4}r = 10\) | M1 A1 (2) |
(a) | $x = 0, y = 0, z = 2$ | B2, 1, 0 (2) | Any 2 out of 3 values correct; All 3 values correct |
(b) | $P - 2x - 4y + \frac{5}{4}r = 10$ | M1 A1 (2) | One equal sign, modulus of coefficients correct. All the right ingredients; cao – condone terms of zero coefficient |
**Total [4]**
---5. While solving a maximising 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
z & $\frac { 1 } { 4 }$ & $- \frac { 1 } { 4 }$ & 1 & $\frac { 1 } { 4 }$ & 0 & 0 & 2 \\
\hline
s & $\frac { 5 } { 4 }$ & $\frac { 7 } { 4 }$ & 0 & $- \frac { 3 } { 4 }$ & 1 & 0 & 4 \\
\hline
t & 3 & $\frac { 5 } { 2 }$ & 0 & $- \frac { 1 } { 2 }$ & 0 & 1 & 2 \\
\hline
P & -2 & -4 & 0 & $\frac { 5 } { 4 }$ & 0 & 0 & 10 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Write down the values of $\mathrm { x } , \mathrm { y }$ and z as indicated by this tableau.
\item Write down the profit equation from the tableau.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 2009 Q5 [4]}}