This question actually relates to a video game, I came across the scenario and I realized I had no idea how to go about solving something like this or even what branch of mathematics it falls under. 

Anyway, the simplified version is as follows:

There are two types of currencies, I will call them currency A and currency B.

You start out with an income of 512 of currency A per second and an income of 36 of currency B per second. 

The goal is to get to 1 million or more of each type of currency at the same time as fast as possible.

Although, in order to speed up your progress you can invest in things that will give you more currency. The things you can invest in and their bonus income are as follows:

Format: Option name, cost, bonus income

* A1, 33 B, +1 A/s (s is seconds)
* A2, 257 B, +8 A/s
* A3, 1025 B, +32 A/s
* A4, 4097 B, +128 A/s
* A5, 16385 B, +512 A/s
* A6, 65537 B, +2048 A/s
* A7, 262145 B, +8192 A/s
* A8, 1000001 B, +32768 A/s
* B1, 4096 A, +1 B/s
* B2, 20480 A, +6 B/s
* B3, 81920 A, +36 B/s
* B4, 262144 A, +216 B/s
* B5, 1000000 A, +1296 B/s

Using these investment options, what is the fastest way to obtain 1 million or more of both currency A and currency B at the same time?

I am most concerned with what TYPE of question this is and HOW to solve it rather than the actual answer. Any help on this would be appreciated.

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Note: Since I am not sure what branch of mathematics this is I put optimization down as the tag, if this tag is incorrect I would appreciate it if someone could add the correct tag.