Which system variable tells how far into the rest of each incomplete plan the optimizer should look to evaluate whether it should be expanded further?

Answer: Option B

This question is about how MySQL's query optimizer decides how much time to spend searching for the best way to execute a query.

The optimizer is like a planner for your database. It figures out the most efficient way to find the data you need. Sometimes, it has to look at a lot of different options, but it can't spend forever on it.

The optimizer_search_depth variable is like a limit on how far the optimizer will look. Think of it like a depth limit for a tree where each branch represents a different way to run the query.

Here's why the other options aren't the answer:
* optimizer_prune_level: This variable affects how the optimizer gets rid of bad options early.
* optimizer_search: This is an older variable that was used to control search strategies.
* optimizer_prune: This isn't a real variable in MySQL.

So the correct answer is Option B: optimizer_search_depth. This variable helps control how far the optimizer will go in finding the most efficient query plan.