Formulating and graphical solution of LPsAQA A-Level Further Maths: Mind map

Exam questions on Formulating and graphical solution of LPs

1. A workshop makes $x$ tables and $y$ chairs each week. Each table needs 4 hours of carpentry and 2 hours of finishing. Each chair needs 2 hours of carpentry and 3 hours of finishing. There are 40 hours of carpentry and 30 hours of finishing available each week. The workshop must make at least twice as many chairs as tables. The profit is £50 per table and £30 per chair, and the workshop wants to maximise its weekly profit.
   Write down the objective function and explain why $x\geq0$ and $y\geq0$ must be included as constraints.2 marks
2. A farmer mixes $x$ kg of feed $X$ and $y$ kg of feed $Y$ for each day. Each kilogram of $X$ has 3 units of protein and 1 unit of fibre and costs £3. Each kilogram of $Y$ has 2 units of protein and 2 units of fibre and costs £4. Each day the mixture must contain at least 24 units of protein and at least 12 units of fibre, and it must weigh at most 10 kg. The farmer wants to minimise the daily cost.
   Explain why a mixture of 5 kg of $X$ and 4 kg of $Y$ is not allowed.2 marks
3. Maximise $P=3x+2y$ subject to $2x+y\leq14$, $x+2y\leq10$, $x\geq0$ and $y\geq0$.
   Find the coordinates of the vertices of the feasible region.3 marks