| Exam Board | OCR |
|---|---|
| Module | FD1 AS (Further Decision 1 AS) |
| Year | 2017 |
| Session | December |
| Marks | 6 |
| Topic | Linear Programming |
| Type | Formulation from word problem |
| Difficulty | Moderate -0.8 This is a straightforward LP formulation question requiring students to define three variables, write one constraint for total area (≥30), one for time (≤8), non-negativity constraints, and identify the cost objective function. It's a standard textbook exercise with clear structure and no conceptual tricks, making it easier than average but not trivial since it requires correct inequality directions and proper formulation syntax. |
| Spec | 7.06a LP formulation: variables, constraints, objective function |
| \cline { 2 - 3 } \multicolumn{1}{c|}{} | Cost | Time |
| Paint | 1.12 | 0.50 |
| Panelling | 4.62 | 0.34 |
| Wallpaper | 1.61 | 0.28 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | 2 | 0 |
Question 2:
2 | 2 | 0 | 3.2 | 2.52 Rahul is decorating a room. He needs to decorate at least $30 \mathrm {~m} ^ { 2 }$ of the walls using paint, panelling or wallpaper.
The cost ( $\pounds$ ) and the time required (hours) to decorate $1 \mathrm {~m} ^ { 2 }$ of wall are shown in the table.
\begin{center}
\begin{tabular}{ | l | c | c | }
\cline { 2 - 3 }
\multicolumn{1}{c|}{} & Cost & Time \\
\hline
Paint & 1.12 & 0.50 \\
\hline
Panelling & 4.62 & 0.34 \\
\hline
Wallpaper & 1.61 & 0.28 \\
\hline
\end{tabular}
\end{center}
Rahul wants to complete decorating the walls in no more than 8 hours and wants to minimise the cost.\\
Set up an LP formulation for Rahul's problem, defining your variables. You are not required to solve this LP problem.
\hfill \mbox{\textit{OCR FD1 AS 2017 Q2 [6]}}