Should you solo focus a skill? Instruct with Professor Expertise? I made a spreadsheet to solve this problem.

Access the spreadsheet here

The sheet uses linear programming to optimize the number of weeks needed to attain two skill ranks.

It assumes that you might solo focus one skill or have both skills set as goals.

Input the amount of points needed in each skill, how much you expect to gain from instructions, and how fast they accrue points from goals.

Bottom line: if you have one skill that needs way more skill points (e.g. you want to S+ it), you should almost always instruct in that skill and not solo-focus it for long. (The sheet will compute how long you need to solo focus it; in reality you would just finish the other skill and then switch to solo focus.) This appears to be true even with professor expertise.

This assumes you want to get both skills in the shortest overall time, not get one skill first for a power spike. It's efficient, not necessarily better for playing the game.

Try different combinations or apply it to different problems you face.