What do we mean by taking the lowest of ZFW; TOW and LW to determine the maximum takeoff weight of the day?
If you know how much fuel you'll need for the flight, then the things that can limit your load (which is really what you're interested in -- how much weight can I put on the airplane today, in terms of passengers + cargo) are:

Empty weight + Payload (ZFW) may not exceed Max ZFW
ZFW + fuel for the flight (TOW) may not exceed MTOW
TOW - fuel burned during flight (i.e. ZFW + fuel reserves) may not exceed MLW

Depending on how much fuel you expect to burn and how much fuel you expect to land with (i.e. reserves), any of these may be the most limiting.
Max ZFW will be limiting for a short flight with minimal reserves required... you're taking off with minimal fuel and landing with minimal fuel, but if you loaded up to max TOW or max LW you'd be well over MZFW.
Max TOW will be limiting with lots of fuel burn planned: if you loaded the pax/cargo to MZFW, the fuel load would put you over MTOW.
Max Landing Weight tends to be most limiting when you need lots of fuel at landing for reserves.  (If you envision an extreme case where you need 5 hours of fuel still in the tanks at landing, if you were close to MZFW you'd be way, way over max landing weight, so the latter rather than the former is most limiting.)
Modern airliners tend to have a range of landing fuel that tends to suggest when MTOW or MLW will be the more limiting.  If you're planning to land with min reserves, you can load to MZFW easily enough (max ZFW + min reserve gas will be &lt; max landing weight); you'll probably be limited by either MZFW or MTOW.  If you need to land with significant reserves, MLW will probably be most limiting for how much cargo/pax you can have.
If you can find a typical empty A-320 weight and typical &quot;good weather&quot; and &quot;bad weather&quot; fuel reserve values (maybe 3t and 7t for the latter), as well as some &quot;short haul&quot; and &quot;long haul&quot; burns (guessing, maybe 3t short haul and 20-25t long haul), you can work out various cases of what load you can accept in each scenario of good/bad wx and short/long haul flight using the equations I described above.
EDIT: The discussion above treats MTOW as a constant, although in reality that isn't necessarily the case: the max takeoff weight on a high, hot, and short runway can be significantly less than the structural max takeoff weight.  The basic math doesn't change, but it's fair to note that MTOW is the lesser of structural MTOW or the performance-limited takeoff weight.  (The various performance limits can be any of a number of things: accelerate-stop, accelerate-go, climb performance, etc.)  For some jets, you can also have a performance limitation of Enroute performance, i.e. being able to clear enroute terrain if an engine fails.  Most modern jets, however, have sufficient performance that this isn't often (or ever) an issue.  But it is the stuff of ground-eval orals.