How can I formulate this multi-objective optimization problem?

Question

Now, for each system $X$ $(X=A,B,C,E)$, my objective is $$\max\min\frac{s_{x_u}}{d_{x_u}}$$ here, $x=a$ for system A, $x=b$ for system B and follows...

and for the whole system, my objective is $$\max\min\frac{s_{X}}{d_{X}}$$

Here, $s_{x_u}$ is a function of optimization variable $a$, i.e.,$s_{x_u}=f(a),$ while $s_{X}$ is a function of optimization variable $z$ and of course $s_{x_u}$, i.e., $s_{X}=f(z,s_{x_u}).$

How can I formulate this optimization problem?

I mean how to have a single objective function.

Ideas

For each system, I can rewrite the objective as $\max t_x$ by adding the following constraint $s_{x_u}\ge t_x d_{x_u}$. So, I now have $\max t_a$, $\max t_b$, $\max t_c$ and $\max t_e$.

Likewise, for the overall system I can reformulate it as $\max t_X$ and adding the following constraints $s_X\ge t_X d_X$, $X=\{A,B,C,E\}$.

So, now the objective function I have is

$$\max t_a\hspace{1mm} \& \max t_b \hspace{1mm} \& \max t_c \hspace{1mm} \& \max t_e \hspace{1mm} \& \max t_X.$$

Is it okay to write $\max t_a+t_b+t_c+t_e+t_X$?