Supplied with what? Chinese forces had very little supplies to begin with. Chinese troops had no experience with industrialied warfare and the troops knows only how to fight WWI battles at the beginning.
You do know why Chiang forced the battle at Shanghai, right? The reason is to force the Japs to go through China horizontally instead of vertically. If the Japs go down from the north plains, they can leverage their vastly more superior mobility and armour to sweep across China vertically like the German did in Europe. If the Japs had to go through China horizontally through Shanghai, they have to go through areas of China that are full of rivers and lakes, which greatly reduce their mobility and give China some breathing room to mobilize.
He leverage the best of what he got because of the point I made above.
They don't have enough bullets because the transportation system was horrible. Chiang mobilize forces from all over China, but large portion of the forces had to get to Shanghai by foot and got wiped out right after they reach their positions because of their poor training (they don't know about preparing their positions for artillery bombardments
Those troops are battle harden troops that are much much better equiped than the Chinese forces during the Japanese invasion. What ever their competences, they couldn't push the American past the 38 parallel due to supply problems, something Chinese forces had to deal with the entire time during the war of resistance. At least they have a stable rear that can produce supplies/materials steadily
Thank you for proving my point. Chiang forced the battle at Shanghai because he thought he could grind down the Japanese there. Instead, he lost his most elite divisions and directly led to the Nanjing Massacre. In the end, China lost more than Japan in the Battle of Shanghai. That is *NOT* what I'd call competence!
Traditionally, China has always been invaded from the north, because that is where the most militarily defensible positions are. That is why the Great Wall was built there. If you read about the Battle of Shanghai, the Japanese Navy refused to take on Shanghai alone, and the Army had to get involved. That means if Chiang had met the IJA in the north, they would likely not have had enough manpower to take on Shanghai.
Again, I would refer you to the defense of the Great Wall. 300k NRA soldiers defended the Wall for months. Are you going to tell me that Chiang could get 300k men there, but couldn't send them enough bullets throughout months of battle? Forget tanks and howitzers, get those guys enough machine guns and mortars and they would've sent the mere 50k Japanese troops packing. Of course, that would've meant equipping troops that were not particularly loyal to Chiang (the reason they were sent north in the first place), and having the risk of Song Zheyuan going warlord.
You mentioned the Japanese having the advantage in the north because of their mobility and armor. Well yes, if by "north" you mean the Central Plains. That is why the Great Wall is crucial. The ROC was not the first Chinese "dynasty" to face an enemy with superior mobility. The Ming fought Mongols and Manchu, both of whom had a lot more cavalry than the Ming. There's a reason why, when Wu Sangui surrendered the Shanhai pass, the Qing were able to sweep south practically unopposed.