Intro Econ Homework Question

I'm quite pleased with the question I just made up:

Suppose you are a central planner in a communist country, and it is your job to set the price of rutabagas.  The first person assigned to this job set a price of 10.  This resulted in 40 tons of rutabagas supplied and 70 tons of rutabagas demanded.  The result was shortages, which led to long lines, which led to riots, which led to the planner getting arrested and shot.  That person's replacement set a price of 20.  This resulted in 80 tons of rutabagas supplied and 60 tons of rutabagas demanded, which led to 20 tons of rutabagas being thrown away to rot, which led to the planner getting arrested and shot.

Assuming that the supply and demand are linear, what price should you set for rutabagas so you do not get arrested and shot?