| Exam Board | Edexcel |
|---|---|
| Module | FD1 AS (Further Decision 1 AS) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Formulation with percentage constraints |
| Difficulty | Standard +0.8 This is a non-trivial linear programming formulation requiring students to translate percentage constraints into algebraic inequalities (0.35 ≤ x/(x+y) ≤ 0.65), which involves algebraic manipulation to linearize them. While the cost objective is straightforward, the percentage constraints elevate this beyond routine formulation questions, requiring careful algebraic reasoning to express them with integer coefficients. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06b Slack variables: converting inequalities to equations |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Minimise \((C=)\ 25x+35y\) | B1 | A correct objective function + minimise |
| Subject to: \((500x+800y \geq 150\,000 \Rightarrow)\ 5x+8y \geq 1500\) | B1 | Translate information into a correct inequality |
| \(\frac{7}{20}(x+y) \leq x\) | M1 | Translating information given into the LHS inequality |
| \(x \leq \frac{13}{20}(x+y)\) | M1 | Translating information given into the RHS inequality |
| Which simplifies to \(7y \leq 13x\) and \(13y \geq 7x\) | A1 | Simplifying to the correct inequalities |
| \(x, y \geq 0\) |
## Question 5:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Minimise $(C=)\ 25x+35y$ | B1 | A correct objective function + minimise |
| Subject to: $(500x+800y \geq 150\,000 \Rightarrow)\ 5x+8y \geq 1500$ | B1 | Translate information into a correct inequality |
| $\frac{7}{20}(x+y) \leq x$ | M1 | Translating information given into the LHS inequality |
| $x \leq \frac{13}{20}(x+y)$ | M1 | Translating information given into the RHS inequality |
| Which simplifies to $7y \leq 13x$ **and** $13y \geq 7x$ | A1 | Simplifying to the correct inequalities |
| $x, y \geq 0$ | | |\begin{enumerate}
\item Jonathan makes two types of information pack for an event, Standard and Value.
\end{enumerate}
Each Standard pack contains 25 posters and 500 flyers.\\
Each Value pack contains 15 posters and 800 flyers.\\
He must use at least 150000 flyers.\\
Between $35 \%$ and $65 \%$ of the packs must be Standard packs.\\
Posters cost 20p each and flyers cost 4p each.\\
Jonathan wishes to minimise his costs.\\
Let x and y represent the number of Standard packs and Value packs produced respectively.\\
Formulate this as a linear programming problem, stating the objective and listing the constraints as simplified inequalities with integer coefficients.
You should not attempt to solve the problem.
\section*{(Total for Question 5 is 5 marks)}
TOTAL IS 40 MARKS
\hfill \mbox{\textit{Edexcel FD1 AS Q5 [5]}}