The simplex algorithmAQA A-Level Further Maths: Mind map

Exam questions on The simplex algorithm

1. Maximise $P=2x+y$ subject to $x+y\leq8$, $3x+y\leq18$, $x\geq0$ and $y\geq0$. The simplex algorithm is to be used, with slack variables $r$ and $s$ added to the first and second constraints.
   Carry out the first iteration. State the values of $x$, $y$ and $P$ after it.2 marks
2. The simplex algorithm is used to maximise $P=2x+3y$ subject to $x+2y\leq14$ and $3x+y\leq18$, with slack variables $r$ and $s$. After the first iteration the equations are $\frac12x+y+\frac12r=7$, $\frac52x-\frac12r+s=11$ and $P-\frac12x+\frac32r=21$.
   Find the pivot row for the next iteration, giving a reason.2 marks
3. Maximise $P=4x+3y$ subject to $2x+y\leq10$, $x+y\leq8$, $x\geq0$ and $y\geq0$. The simplex algorithm is to be used with slack variables $r$ and $s$ added to the first and second constraints.
   Write down the initial simplex tableau as equations, and state which entry is the pivot in the first iteration, with a reason.3 marks