Linearization of a scheduling objective function

I am trying to maximize the workload per employee.

An example:

• $e$ the index of an employee
• $j$ the index of a project
• decision variable: $x_{e,j} \in \mathbb{Z}$ and $0 \leq x_{e,j} \leq 100$ deciding with how much percent an employee may work on a project. (Yes it is possible that an employee works on a project with 40%. The remaining 60% should get covered from someone else and all projects should get covered but this is not a part of this problem.)
• decision variable: $y_e \in \{0,1\}$ deciding if employee e is working

I had in mind something like the following as a part of the objective function $$ \max\sum\limits_{e,j}\frac{x_{e,j}}{y_e}$$

The problem is that this is not linear.

Example: $\frac{160}{3} < \frac{160}{2}$ thus 2 employees whould be preferred instead of 3.

Note:

The following constraint has to hold,

$$ \sum\limits_e x_{e,j} = 1 \ \ \forall \ \ j $$

implying that all projects have to get covered.