For what it's worth, this isn't how "supply and demand" works in economics.
The idea is that a given firm is already producing as much as they can at that price. There's not usually a ton of slack just laying around that could respond to a spike in demand. For instance, my wife who works at a soap factory right now, has seen a ton of demand. They would love to increase production to accommodate but it's just not immediately possible, without retooling the factory. They're managing to increase supply a little, by not offering as many varieties of scents and such, but that's the extent of what they can do immediately.
The reason prices increase with an increase in demand, according to standard economics orthodoxy, is because that allows more firms to enter the market, as well as existing firms to do less efficient things (more workers, more expensive supply chain, etc), to meet that demand.