I am trying to determine the relative concentrations of $\ce{U1}$, $\ce{U2}$, and $\ce{E}$ when the following reaction is at steady state. Note that $k_t$ is the zero order rate constant of new $\ce{U1}$ entering the system and $k_d$ is the first order rate constant of substances leaving the system.
$k_1$ and $k_2$ are the first order rate constant for the forward and reverse reaction, respectively, of $\ce{U1}$ turning into $\ce{U2}$, and $k_e$ is the first order rate constant for $\ce{U2}$ reacting to $\ce{E}$. First order reactions are all first order in the respective reactant.
All the individual rate constants are known but the concentrations are not.
Can anyone point me in the right direction for how to determine the relative concentrations at steady state? I'm imagining an equation or set of equations such that when values for each rate constant are plugged in, the concentrations of the products are determined.