| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Integer solution optimization |
| Difficulty | Moderate -0.3 This is a standard D1 linear programming question requiring graphical representation, objective line method, and integer solution adjustment. While it involves multiple constraints and steps, all techniques are routine textbook procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06b Slack variables: converting inequalities to equations7.06d Graphical solution: feasible region, two variables7.06f Integer programming: branch-and-bound method |
5. A linear programming problem in $x$ and $y$ is described as follows.
Maximise $\quad P = 2 x + 3 y$\\
subject to
$$\begin{aligned}
x & \geqslant 25 \\
y & \geqslant 25 \\
7 x + 8 y & \leqslant 840 \\
4 y & \leqslant 5 x \\
5 y & \geqslant 3 x \\
x , y & \geqslant 0
\end{aligned}$$
\begin{enumerate}[label=(\alph*)]
\item Add lines and shading to Diagram 1 in the answer book to represent these constraints. Hence determine the feasible region and label it R .
\item Use the objective line method to find the optimal vertex, V, of the feasible region. You must clearly draw and label your objective line and the vertex V.
\item Calculate the exact coordinates of vertex V.
Given that an integer solution is required,
\item determine the optimal solution with integer coordinates. You must make your method clear.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2014 Q5 [11]}}