Learn Farsi: برای اینکه برنامه اجراپذیر باشد، مسیرها باید تغییرپذیر باشند. - For the schedule to be feasible, the routes must be changeable.

The suffix پذیر comes from the present stem of پذیرفتن (to accept). When added to a noun, it means "capable of" or "susceptible to" that action or state, very similar to the English suffixes "-able" or "-ible". Therefore, تغییر (change) becomes تغییرپذیر (changeable), and اجرا (execution or implementation) becomes اجراپذیر (executable or feasible).

Why are both verbs in this sentence in the subjunctive mood (باشد and باشند)?

The first verb, باشد, is in the subjunctive because of the conjunction برای اینکه (in order that / so that). This phrase expresses a purpose or hypothetical intent, which triggers the subjunctive. The second verb, باشند, is triggered by the modal verb باید (must), which always requires the following verb to take the subjunctive mood.

Since مسیرها (routes) is an inanimate plural noun, shouldn't its verb be singular rather than the plural باشند?

In Farsi, inanimate plural subjects certainly can take a singular verb, and doing so is extremely common in everyday speech. However, in formal, written, or slightly more elevated Farsi (which this sentence represents), it is perfectly correct and often preferred to use a plural verb like باشند to strictly agree with a plural subject. Both choices are grammatically valid.

Could you just use ممکن instead of to mean "feasible" here?