I know how to formulate the dual problem to a standard minimisation Linear Program. However I came across this example which confused me slightly.
Write down the dual problem of:
Minimise $3x_1+5x_2+6x_3$
Subject to:
$2x_1+4x_2+7x_3-x_4=5$
$-3x_1+2x_2-6x_3+x_5=-4$
$x_1,x_2,x_3,x_4,x_5\geqslant0$
The answer to this is:
Maximise $5y_1-4y_2$
Subject to:
$2y_1-3y_2\le3$
$4y_1+2y_2\le5$
$7y_1-6y_2\le6$
$-y_1\le0, y_2\le0$
It is just the last line of the solution that confuses me, I assumed it was always $y_1\ge0, y_2\ge0$ so this would become $-y_1\le0, -y_2\le0$