I have these two constraints :
$z \leq My$
$t \leq M'y $
where $z$ and $t$ are two integer variables $ z, t\geq 0$, $y$ is a binary variable, and $M$, $M'$ are two big numbers.
So basically these constraints ensure that if $y = 1$ then $z, t \leq M , M'$ respectively, otherwise $z,t = 0$.
However these constraints won't give me a positive value for $t$ if $z > 0$.
My question is : how to connect variables $z$ and $t$ to ensure that if $z > 0$ then $t > 0$ .
The logical constraint that I want to write is as following:
if $y= 1$ then $z >0$ and $t>0$ .