Suppose you have N factories. This constitutes the 0th generation. Each factory can produce either a widget or another factory.
So, for example, if N = 2, then you have two factories F1 and F2. If you decide that each produces a widget, then in generation 1 you'd have 2 factories, F1 and F2, and 2 widgets. If you decide that each produces a factory, then in generation 1 you'd have 4 factories, F1 through F4, and 0 widgets.
1.) Is there an ideal strategy that maximizes widgets at every generation?
2.) What is the ideal strategy to maximize the number of widgets by generation k?