I am looking for an optimization algorithm for a program I am trying to write. To keep the question as simple as possible, I have crafted it into a story.
A carpenter receives an order for N chairs. He can only build 1 chair per day. He can also build a machine that can either build one chair per day, or can build another machine (a chair and a machine each have a one day build time). How can I optimize for the fewest amount of days needed to build N chairs? How would this be represented mathematically?
For my purposes the "day" could be as small as a fraction of a second, and N can be as large as maybe 100,000.
Thank you in advance for your help!