| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | The Simplex Algorithm |
| Type | Perform one Simplex iteration |
| Difficulty | Moderate -0.8 This is a routine, procedural Simplex algorithm question requiring standard mechanical steps: setting up the initial tableau, performing one pivot operation as directed, and reading off the solution. It tests only recall and execution of the algorithm with no problem-solving or insight required, making it easier than average A-level material. |
| 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 objective7.07d Simplex terminology: basic feasible solution, basic/non-basic variable7.07e Graphical interpretation: iterations as edges of convex polygon7.07f Algebraic interpretation: explain simplex calculations7.07g |
\begin{enumerate}
\item A linear programming problem is defined as follows:
\end{enumerate}
$$\begin{array} { l l }
\text { Maximise } & P = 3 x + 3 y + 4 z \\
\text { subject to } & x + 2 y + z \leq 30 \\
& 5 x + y + 3 z \leq 60 \\
\text { and } & x \geq 0 , y \geq 0 , z \geq 0 .
\end{array}$$
(a) Display the problem in a Simplex Tableau.\\
(b) Starting with a pivot chosen from the $z$-column, perform one iteration of your tableau.\\
(c) Write down the resulting values of $x , y , z$ and $P$ and state with a reason whether or not these values give an optimal solution.\\
\hfill \mbox{\textit{OCR D2 Q1 [8]}}