| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Graphical optimization with objective line |
| Difficulty | Standard +0.3 This is a standard D1 linear programming question requiring constraint formulation from a word problem, graphical solution, and interpretation. The area constraint requires converting units (cm to m) and the setup is straightforward once understood. Part (iv) is open-ended discussion requiring no calculation. Slightly above average due to the multi-step nature and unit conversion, but follows a well-practiced template for D1 students. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06d Graphical solution: feasible region, two variables |
4 A wall 4 metres long and 3 metres high is to be tiled. Two sizes of tile are available, 10 cm by 10 cm and 30 cm by 30 cm .\\
(i) If $x$ is the number of boxes of ten small tiles used, and $y$ is the number of large tiles used, explain why $10 x + 9 y \geqslant 1200$.
There are only 100 of the large tiles available.\\
The tiler advises that the area tiled with the small tiles should not exceed the area tiled with the large tiles.\\
(ii) Express these two constraints in terms of $x$ and $y$.
The smaller tiles cost 15 p each and the larger tiles cost $\pounds 2$ each.\\
(iii) Given that the objective is to minimise the cost of tiling the wall, state the objective function. Use the graphical approach to solve the problem.\\
(iv) Give two other factors which would have to be taken into account in deciding how many of each tile to purchase.
\hfill \mbox{\textit{OCR MEI D1 2010 Q4 [16]}}