Moderate -0.8 This is a straightforward linear programming formulation requiring translation of verbal constraints into inequalities. All constraints are direct translations with minimal algebraic manipulation (e.g., '25% of total' becomes x ≥ 0.25(x+y), which simplifies to 3x ≥ y). The objective function is immediate. This is easier than average as it's a standard D1 textbook exercise with no conceptual subtlety or problem-solving required beyond routine constraint identification.
8. A manufacturer of frozen yoghurt is going to exhibit at a trade fair. He will take two types of frozen yoghurt, Banana Blast and Strawberry Scream.
He will take a total of at least 1000 litres of yoghurt.
He wants at least \(25 \%\) of the yoghurt to be Banana Blast. He also wants there to be at most half as much Banana Blast as Strawberry Scream.
Each litre of Banana Blast costs \(\pounds 3\) to produce and each litre of Strawberry Scream costs \(\pounds 2\) to produce. The manufacturer wants to minimise his costs.
Let \(x\) represent the number of litres of Banana Blast and \(y\) represent the number of litres of Strawberry Scream.
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.
(Total 6 marks)
8. A manufacturer of frozen yoghurt is going to exhibit at a trade fair. He will take two types of frozen yoghurt, Banana Blast and Strawberry Scream.
He will take a total of at least 1000 litres of yoghurt.\\
He wants at least $25 \%$ of the yoghurt to be Banana Blast. He also wants there to be at most half as much Banana Blast as Strawberry Scream.
Each litre of Banana Blast costs $\pounds 3$ to produce and each litre of Strawberry Scream costs $\pounds 2$ to produce. The manufacturer wants to minimise his costs.
Let $x$ represent the number of litres of Banana Blast and $y$ represent the number of litres of Strawberry Scream.
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.\\
(Total 6 marks)\\
\hfill \mbox{\textit{Edexcel D1 2014 Q8 [6]}}