About supplies in North Africa:
https://en.wikipedia.org/wiki/Western_Desert_Campaign#Aftermath
So 500 trucks carrying 1 tonne could support two divisions up to 100 km. I was not too far from reality.
Ben Gardane - Tripoli is 200 km, so French have to gather at least 1,000 trucks to have the minimum logistic to reach Tripoli after breaking the front.
Of course, this is not enought to crush the Italian (5 to 6 divisions) but the constant shelling and the aerial bombing will reduce considerably the potential and morale of the Italian army while denying any big movment. The objective of French will be to fix, encircle and destroy the big units. Bombing coastal road, railway and Italian positions during several weeks will be a good start point.
This assumes the Italians sit passively in the border positions & the French can move their main force from the interior Mareth position to the border. I cant say at this point how aggressive the Italians might have been. There is a possibility they ould attempt to secure the region between the border & the main French defense zone. Perhaps someone has information of the Italian plans & we can dismiss this out of hand? But, were the Italians field army ordered forward it would have some advantages for the French. The logistics situation is reversed allowing a more efficient build up for the French & creating problems for the Italians. I suspect the Italian logistics capability wont be sufficient for moving their full army present across southern Tunisia in June-July. If ordered to advance this could mean a partial force of advance guards from each corps, or some sort of light corps that can be sustained. If this is the case what we'd see is some sort of broad but thin battle between them and the French screening forces, plus reinforcements for each side.
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Of course, this is not enought to crush the Italian (5 to 6 divisions) but the constant shelling and the aerial bombing will reduce considerably the potential and morale of the Italian army while denying any big movment. The objective of French will be to fix, encircle and destroy the big units. Bombing coastal road, railway and Italian positions during several weeks will be a good start point.
Its very unlikely a French attack into the main Italian defense zone would depend on some sort of flanking maneuver in the interior. Between the terrain and a look at the French strengths a methodical attack nearer the coast would be the plan. Raids around the Italian flank & diversions could be made. The goal would be to gain the better coastal road/s & threaten the Italians with having their communications cut. The logical thing at that point is for the Italians to retreat to a intermediate position nearer to Tripoli. A short pursuit or exploitation to disrupt that would be within the capability of the French mobile forces. Fifty or 100 kilometers may be practical, & if they are stalled part way it will not be long before the artillery catches up and fresh air attacks organized.
If the French are lucky the Italians have difficulty coping with such withdrawal under attack. Corps that have lost significant equipment and prisoners & declining morale may be easier to break when the intermediate positions or the main Tripoli defense is attacked.