Easy -1.2 This is a straightforward linear programming formulation question requiring students to define variables, write an objective function (maximise 0.2b + 0.15c), and express three simple constraints (b + c ≤ 200, b ≥ 2c, b,c ≥ 0). It's a standard textbook exercise with no problem-solving insight required, just direct translation of words into mathematical inequalities, making it easier than average.
A Young Enterprise Company decides to sell two types of cakes at a breakfast club.
The two types of cakes are blueberry and chocolate.
From its initial market research, the company knows that it will:
• sell at most 200 cakes in total
• sell at least twice as many blueberry cakes as they will chocolate cakes
• make 20p profit on each blueberry cake they sell
• make 15p profit on each chocolate cake they sell.
The company's objective is to maximise its profit.
Formulate the Young Enterprise Company's situation as a linear programming problem.
[4 marks]
Question 6:
6 | Defines two variables to represent
the number of blueberry cakes
and the number of chocolate
cakes | 3.1b | B1 | Let x = number of blueberry cakes
made
Let y = number of chocolate cakes
made
Maximise 20x + 15y
subject to x + y ≤ 200
x ≥ 2y
x ≥ 0, y ≥ 0
x and y are integers
Obtains one of x + y ≤ 200, x ≥ 2y
or 20x + 15y OE
Condone strict inequality | 1.1a | M1
Obtains x + y ≤ 200 and x ≥ 2y | 1.1b | A1
Formulates the linear
programming problem correctly
with a statement of maximising a
correct objective function and all
constraints fully correct | 2.5 | A1
Question total | 4
Q | Marking instructions | AO | Marks | Typical solution
A Young Enterprise Company decides to sell two types of cakes at a breakfast club.
The two types of cakes are blueberry and chocolate.
From its initial market research, the company knows that it will:
• sell at most 200 cakes in total
• sell at least twice as many blueberry cakes as they will chocolate cakes
• make 20p profit on each blueberry cake they sell
• make 15p profit on each chocolate cake they sell.
The company's objective is to maximise its profit.
Formulate the Young Enterprise Company's situation as a linear programming problem.
[4 marks]
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2024 Q6 [4]}}