Graphical solution of linear programsEdexcel International A Level Maths: Mind map

Exam questions on Graphical solution of linear programs

1. A furniture company makes $x$ desks and $y$ chairs each day. The company wants to maximise its daily profit $P=5x+4y$ (in hundreds of pounds), subject to the constraints $x+y\le10$ (worker hours), $3x+y\le18$ (workshop space), $x\ge0$ and $y\ge0$.
   The feasible region has vertices $(0,0)$, $(6,0)$, $(4,6)$ and $(0,10)$. Use the vertex method to find the maximum value of $P$ and the values of $x$ and $y$ at which it occurs.2 marks
2. A school canteen mixes $x$ kg of ingredient X and $y$ kg of ingredient Y in each batch. The cost is $C=4x+3y$ pence, which is to be minimised, subject to $2x+y\ge12$ (energy), $x+2y\ge9$ (protein), $x+y\le10$ (tank capacity), $x\ge0$ and $y\ge0$.
   Show that the lines $2x+y=12$ and $x+2y=9$ meet at $(5,2)$, and find the value of $C$ there.2 marks
3. A potter makes $x$ mugs and $y$ bowls each day. The clay available gives $2x+3y\le14$ and the kiln time available gives $4x+y\le15$, with $x\ge0$ and $y\ge0$. The profit is $P=5x+4y$ pounds, which is to be maximised.
   Show that the lines $2x+3y=14$ and $4x+y=15$ meet at $(3.1,\,2.6)$, and find the value of $P$ there.3 marks