How can I solve this LP problem:
Maximize p=x subject to :
x+y <=30
x-2y <= 0
2x+y >=30
x>=0 , y>=0
using simplex method?
How can I solve this LP problem:
Maximize p=x subject to :
x+y <=30
x-2y <= 0
2x+y >=30
x>=0 , y>=0
using simplex method?
I am guessing you are asking how to write the LP in 'standard form'?
The general idea here is if you have a constraint of the form $a_1 x_1 + \cdots + a_n x_n \leq 0$, then you replace this constraint by an equality constraint of the form $a_1 x_1 + \cdots + a_n x_n = -s$, where $s$ is a new variable (called a slack variable) with the constraint $s \geq 0$. It is easy to see that these are equivalent (as long as you now optimize over the new variables as well).
So, your problem would become:
Maximize p=x subject to :
$x+y = 30-s_1$
$x-2y = -s_2$
$2x+y = 30+s_3$
$x \geq 0 , y\geq 0$ $s_1 \geq 0 , s_2\geq 0, s_3 \geq 0$