Looking at the various system maps, if the Commonwealth considers Platea within mining exploitation distance then perhaps it will reactivate its geo survey vessels and survey those new systems to the 'North'.
In the Platea system itself, I would think that between
Plataea-A II - Moon 5
Duranium 1,264,043 Acc: 0.8
Neutronium 221 Acc: 0.5
Corbomite 497,019 Acc: 0.7
Tritanium 2,249,994 Acc: 0.7
Boronide 119,019 Acc: 0.7
Mercassium 1,742,393 Acc: 0.8
Vendarite 476,095 Acc: 0.6
Sorium 632,016 Acc: 1
Uridium 140,617 Acc: 0.9
Corundium 11,021 Acc: 0.5
Gallicite 562,496 Acc: 0.5
and
Plataea-A II - Moon 12
Duranium 1,800 Acc: 1
Corbomite 441 Acc: 1
Tritanium 2,500 Acc: 1
Boronide 8,464 Acc: 1
Mercassium 3,721 Acc: 1
Vendarite 5,929 Acc: 1
Corundium 324 Acc: 1
Gallicite 1,296 Acc: 1
It would actually be fairly close. Moon 12 has higher concentrations of the minerals most in demand, Duranium, Mercassium and Gallicite. It would be fairly simple for one freighter or convoy to pick up minerals from both moons, and starting some automated mines on Moon 12 and shipping the larger quantity to Moon 5 later would fix the current shortages slightly faster.