| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Graphical optimization with objective line |
| Difficulty | Moderate -0.8 This is a standard textbook linear programming question requiring routine graphical methods: plot constraints, identify feasible region, test vertices. The constraints are simple linear inequalities, and the integer requirement in part (ii) adds minimal complexity. This is below average difficulty as it's purely procedural with no problem-solving insight needed. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06d Graphical solution: feasible region, two variables |
2 Consider the following linear programming problem.\\
Maximise
$$\mathrm { P } = 6 x + 7 y$$
subject to
$$\begin{aligned}
& 2 x + 3 y \leqslant 9 \\
& 3 x + 2 y \leqslant 12 \\
& x \geqslant 0 \\
& y \geqslant 0
\end{aligned}$$
(i) Use a graphical approach to solve the problem.\\
(ii) Give the optimal values of $x , y$ and P when $x$ and $y$ are integers.
\hfill \mbox{\textit{OCR MEI D1 2008 Q2 [8]}}