| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2004 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Graphical feasible region identification |
| Difficulty | Moderate -0.3 This is a standard D1 linear programming question with routine graphical methods. Part (a) requires plotting four linear inequalities and identifying the feasible region—a core skill practiced extensively. Part (b) involves minimizing an objective function by testing vertices, yielding fractional answers. Part (c) adds the common twist of requiring integer solutions for maximization. While multi-part with 13 marks total, each component follows textbook procedures without requiring novel insight or complex reasoning, making it slightly easier than the average A-level question across all modules. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06d Graphical solution: feasible region, two variables |
Becky's bird food company makes two types of bird food. One type is for bird feeders and the other for bird tables. Let $x$ represent the quantity of food made for bird feeders and $y$ represent the quantity of food made for bird tables. Due to restrictions in the production process, and known demand, the following constraints apply.
$$x + y \leq 12,$$
$$y < 2x,$$
$$2y \geq 7,$$
$$y + 3x \geq 15.$$
\begin{enumerate}[label=(\alph*)]
\item On the axes provided, show these constraints and label the feasible region $R$. [5]
\end{enumerate}
The objective is to minimise $C = 2x + 5y$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Solve this problem, making your method clear. Give, as fractions, the value of $C$ and the amount of each type of food that should be produced. [4]
\end{enumerate}
Another objective (for the same constraints given above) is to maximise $P = 3x + 2y$, where the variables must take integer values.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Solve this problem, making your method clear. State the value of $P$ and the amount of each type of food that should be produced. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2004 Q7 [13]}}