# Production maximization problem

I have the following simplified problem, which I think it is a maximization problem with multiple options, constraints, and a time factor:

• Factory A, initial number known (e.g. 8), cost 11000, unitary daily
output 5

• Factory B, initial number known (e.g. 3), cost 7000

• Catalyzer, cost 3000. It reduces cost of building A or B by 10% for
each unit of catalyzer. The catalyzer bonus is permanent and additive with more catalyzer.

Factory A can produce Factory A, Factory B, or catalyzer.

Besides, the following conversions are possible (conversion cost in brackets): Factory A -> Factory B (4000) Factory B -> Factory A (9000)

Only up to 15 A factories can work simultaneously in producing A, B, or catalyzer.

Example: 8 factories A, with an output of 5, can produce another factory A, in 11000 / (8 * 5) = 275 days.

The objective is to maximize the number of B factories at different time horizons: 2, 3, 4, 5, and 6 years from the present.

I would appreciate any comments on how to approach this problem, what are the techniques I should apply, and the best software that I can use to solve this. Thank you.