AQA Further AS Paper 2 Discrete 2019 June — Question 3 4 marks

Exam BoardAQA
ModuleFurther AS Paper 2 Discrete (Further AS Paper 2 Discrete)
Year2019
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear Programming
TypeFormulation from word problem
DifficultyModerate -0.8 This is a straightforward linear programming formulation with two variables, simple constraints from resource limits, and a clear objective function (maximize total cakes). It requires only direct translation of the word problem into mathematical inequalities with no conceptual subtlety or problem-solving insight needed.
Spec7.06a LP formulation: variables, constraints, objective function
3 Manon makes apple cakes and banana cakes. Each apple cake is made with 3 eggs and 100 grams of flour. Each banana cake is made with 2 eggs and 150 grams of flour. Manon has 36 eggs and 1500 grams of flour.
Manon wants to make as many cakes as possible.
Formulate Manon's situation as a linear programming problem, clearly defining any variables you introduce.
Question 3:
AnswerMarks Guidance
AnswerMark Guidance
\(x =\) number of apple cakes, \(y =\) number of banana cakesB1 Defines two variables representing the number of apple cakes and number of banana cakes
One correct non-trivial constraint, e.g. \(3x + 2y \leq 36\) or \(100x + 150y \leq 1500\)M1 Condone strict inequality
Both constraints correct: \(3x + 2y \leq 36\) and \(100x + 150y \leq 1500\)A1 Condone strict inequality
Maximise \(P = x + y\) subject to all constraints fully correct, including \(x \geq 0\), \(y \geq 0\), \(x, y\) are integerA1 Condone \(x, y\) are integer missing
Total: 4 marks
## Question 3:

| Answer | Mark | Guidance |
|--------|------|----------|
| $x =$ number of apple cakes, $y =$ number of banana cakes | B1 | Defines two variables representing the **number of** apple cakes and **number of** banana cakes |
| One correct non-trivial constraint, e.g. $3x + 2y \leq 36$ or $100x + 150y \leq 1500$ | M1 | Condone strict inequality |
| Both constraints correct: $3x + 2y \leq 36$ and $100x + 150y \leq 1500$ | A1 | Condone strict inequality |
| Maximise $P = x + y$ subject to all constraints fully correct, including $x \geq 0$, $y \geq 0$, $x, y$ are integer | A1 | Condone $x, y$ are integer missing |

**Total: 4 marks**
3 Manon makes apple cakes and banana cakes.

Each apple cake is made with 3 eggs and 100 grams of flour. Each banana cake is made with 2 eggs and 150 grams of flour.

Manon has 36 eggs and 1500 grams of flour.\\
Manon wants to make as many cakes as possible.\\
Formulate Manon's situation as a linear programming problem, clearly defining any variables you introduce.\\

\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2019 Q3 [4]}}
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