I want the max of:
$100-(2x_1+3x_2+4x_3+5x_4+6x_5+7x_6)$
I am given 5 inequalities:
$x_1+x_4\le6$
$x_2+x_5\le8$
$x_3+x_6\le7$
$x_1+x_2+x_3\le9$
$x_4+x_5+x_6\le11$
and
$x_1+x_2+x_3+x_4+x_5+x_6\ge0$
It seems obvious that i want the most of $x_1$, and the least of $x_6$ within my constraints, but I am having trouble setting up the set of equations properly. I read about using an extra variable for each inequality to turn it into an equality, but then I think I'll have 12 or 13 equations to solve.
Is there some next step that I should take to solve this?