# Using 'Reduce' to solve a set of inequalities, specified by a list

I have a two lists $LHS$ and $RHS$, both of size $n$. I want to solve a system of inequalities of the form:

$$LHS[1] \leq RHS[1]$$

$$LHS[2] \leq RHS[2]$$

$$LHS[3] \leq RHS[3]$$

$$\vdots$$

$$LHS[n] \leq RHS[n]$$

We assume that:

Each $LHS[i]$ is a linear equation in $m$ variables, say: $\alpha_{1}, \dots, \alpha_{m}$ and each $RHS[i]$ is a linear equation in $m$ variables, say: $\beta_{1}, \dots, \beta_{m}$.

We need to solve for $\alpha_{1}, \dots, \alpha_{m}$, $\beta_{1}, \dots, \beta_{m}$, which are positive integers.

Take m=2. To solve a single inequality (for some $i$ between $1$ and $n$) I know that I need to enter:

Reduce[LHS[[i]]<=RHS[[i]],{[\alpha]0,[\alpha]1,[\beta]0,[\beta]1}]

(I haven't put the constrains to make the code simpler)

But, if I need to solve all the inequalities, how do I input a list in 'Reduce' ?