Linear programmingIB MYP Maths Extended: Mind map

Exam questions on Linear programming

1. A minibus carries $x$ adults and $y$ children. It can carry at most 14 people in total, there must be at least 2 adults, and the number of children can be at most three times the number of adults.
   Determine whether 5 adults and 9 children can travel in the minibus. Give a reason.2 marks
2. A workshop makes $x$ tables and $y$ chairs each week. The weekly limits are $2x+y\le16$ (wood) and $x+2y\le14$ (labour hours), with $x\ge0$ and $y\ge0$. The profit is $P=30x+20y$ dollars. The feasible region has vertices $(0,0)$, $(8,0)$ and $(0,7)$, plus one more vertex where the two boundary lines meet.
   Show that the point $(8,7)$ is not in the feasible region.2 marks
3. A student investigates how the best choice changes when the objective function changes. The feasible region is defined by $x\ge0$, $y\ge0$, $x\le6$, $y\le5$ and $x+y\le8$. The objective is to maximise $P=x+ky$, where $k$ is a positive constant.
   Find the coordinates of the two vertices of the feasible region that lie on the line $x+y=8$. Find the maximum value of $P$ when $k=2$, and the vertex where it occurs.3 marks