Graphical solution of linear programsEdexcel A-Level Further Maths: Mind map

Exam questions on Graphical solution of linear programs

1. A cleaning company makes $x$ litres of cleaner A and $y$ litres of cleaner B each hour. The constraints are $2x+y\le12$ and $x+2y\le10$, with $x\ge0$ and $y\ge0$. The profit in pounds is $P=5x+4y$. The quantities do not need to be whole numbers.
   Find the maximum profit.2 marks
2. A zoo buys $x$ kg of feed X and $y$ kg of feed Y each week. The requirements are $x+y\ge8$ (total mass) and $2x+5y\ge30$ (protein units), with $x\ge0$ and $y\ge0$. The weekly cost in pounds is $C=3x+4y$, which the zoo wishes to minimise. Unless stated otherwise, feed can be bought in any quantity.
   The zoo can now only buy whole numbers of kilograms of each feed. Find the minimum cost and the quantities that give it.2 marks
3. A joiner makes $x$ shelves and $y$ stools each week. The wood constraint is $4x+3y\le26$ and the time constraint is $x+2y\le10$, with $x\ge0$ and $y\ge0$. Each shelf gives £3 profit and each stool gives £2 profit, so the weekly profit is $P=3x+2y$ pounds.
   Use the vertex method to find the maximum profit if shelves and stools did not need to be whole numbers.3 marks