How to linearise the constraint with a product term? I would like to linear the following constraint
$$y\cdot \sum_{i=1}^{N}\mu_ix_i \geq M$$
where $y$ is a positive integer variable, $x_i \in \{0,1\}, i =1,...,N$ are binary variables, $\mu_i, i =1,...,N$ and $M$ are positive constants. 

Thank you.
If $D$ is a sufficiently large constant:

$$\begin{array}{l}
\sum_i \mu_i y_i \geq M \\
0\leq y_i \leq Dx_i \\
0\leq y-y_i\leq D(1-x_i)
\end{array}
$$

Then $x_i=0$ forces $y_i=0$ and $x_i=1$ forces $y_i=y$.
As long as the $x_i$ are not all zero, this inequality can always be satisfied by taking $y$ large enough.  So this is equivalent to $\sum_i x_i \geq 1$.