| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear Programming |
| Type | Formulation from word problem |
| Difficulty | Easy -1.3 This is a straightforward linear programming formulation requiring direct translation of verbal constraints into inequalities and an objective function. It involves no problem-solving insight, just systematic application of a standard D1 technique with clearly stated constraints that map directly to mathematical expressions. |
| Spec | 7.06a LP formulation: variables, constraints, objective function7.06b Slack variables: converting inequalities to equations |
| Answer | Marks | Guidance |
|---|---|---|
| Maximise (P=) \(0.2a + 0.15b\) or \(20a + 15b\) o.e. | B1 B1 | (2 marks) |
| Answer | Marks |
|---|---|
| B1 B2, 1, 0 B1 B1 | (5 marks) |
Maximise (P=) $0.2a + 0.15b$ or $20a + 15b$ o.e. | B1 B1 | (2 marks) |
Subject to
$$a + b \leq 800$$
$$a \geq 2b$$
$$50 \leq b \leq 100$$
$$a \geq 0$$
| B1 B2, 1, 0 B1 B1 | (5 marks) |
**Guidance:**
- 1B1: 'Maximise'
- 2B1: ratio of coefficients correct
- 3B1: cao
- 4B1: ratio of coefficients of $a$ and $b$ correct.
- 5B1: inequality correct way round i.e. $a \geq b$
- 6B1: cao accept < – accept two separate inequalities here
- 7B1: cao
**Note on penalties:**
- Penalise < and > only once with last B mark earned
- Be generous on letters a, b, A, B, x, y etc and mixed, but remove last B mark earned if inconsistent or 3 letters in the ones marked.
**Total for Q8: 7 marks**8. Class 8 B has decided to sell apples and bananas at morning break this week to raise money for charity. The profit on each apple is 20 p , the profit on each banana is 15 p . They have done some market research and formed the following constraints.
\begin{itemize}
\item They will sell at most 800 items of fruit during the week.
\item They will sell at least twice as many apples as bananas.
\item They will sell between 50 and 100 bananas.
\end{itemize}
Assuming they will sell all their fruit, formulate the above information as a linear programming problem, letting $a$ represent the number of apples they sell and $b$ represent the number of bananas they sell.
Write your constraints as inequalities.\\
(Total 7 marks)\\
\hfill \mbox{\textit{Edexcel D1 2008 Q8 [7]}}