Problem I'm trying to figure out
I'm posting this here because I imagine it is a problem involving maximising or minimising a multivariable function. Hence calculus would be useful to solve it but I was never good at turning worded problems into mathematical expressions.
This is just for fun, its not homework or anything but the problem Iím trying to work out is this.
Imagine that you are the owner of a shipyard and are trying to build the most ships in the shortest amount of time. Each ship takes 20min to build initially. However the shipyard can be upgraded to halve the time it takes to build a ship. The first upgrade takes 10s to complete and each subsequent upgrade takes double the time as the last. While the shipyard is upgrading no ships can be produced. Finally to halve the next upgrade time of the shipyard your construction facility can be upgraded. The construction facility's first upgrade takes 10s to complete and doubles every level thereafter. Only one building at a time can be upgraded but while the construction facility is being upgraded ships can be produced at the shipyard. In what order should you produce your ships and upgrade your facilities in order to maximise the amount of ships you can produce in the smallest amount of time.
(for example should you build 5 ships while upgrading your construction facility 5 times, then upgrade the shipyard 5 times and repeat?)