| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matchings and Allocation |
| Type | Linear programming formulation for assignment |
| Difficulty | Easy -1.2 This is a straightforward formulation exercise requiring students to translate a standard assignment problem into LP form. It involves routine application of a template (binary variables for assignments, objective function summing costs, constraints ensuring one-to-one matching) with no problem-solving or novel insight required. The structure is simpler than typical multi-step calculus questions. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06b Slack variables: converting inequalities to equations7.06c Working with constraints: algebra and ad hoc methods |
| \cline { 2 - 4 } \multicolumn{1}{c|}{} | Maths | English | Verbal |
| Team 1 | 3 | 9 | 2 |
| Team 2 | 4 | 7 | 1 |
| Team 3 | 5 | 8 | 3 |
| Answer | Marks |
|---|---|
| D | DG DH |
| E | EG EH |
| F | FG FH |
Question 2:
D | DG DH
E | EG EH
F | FG FH2. A school entrance examination consists of three papers - Mathematics, English and Verbal Reasoning. Three teams of markers are to mark one style of paper each. The table below shows the average time, in minutes, taken by each team to mark one script for each style of paper.
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & Maths & English & Verbal \\
\hline
Team 1 & 3 & 9 & 2 \\
\hline
Team 2 & 4 & 7 & 1 \\
\hline
Team 3 & 5 & 8 & 3 \\
\hline
\end{tabular}
\end{center}
It is desired that the scripts are marked as quickly as possible.\\
Formulate this information as a linear programming problem.
\begin{enumerate}[label=(\alph*)]
\item State your decision variables.
\item Write down the objective function in terms of your decision variables.
\item Write down the constraints, explaining what each one represents.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 Q2 [7]}}