You are correct for the most part Evan. If domestic production is more expensive then foreign production before the tariffs, domestic producers only have to beat the foreign price after the tariff. To make matters worse, there could effectively be a price floor installed with a tariff as domestic producers only have to have prices as low as the foreign products ($15 in your example). This creates a shortage, which not only increases prices, but reduces the quantity of the good (and standard of living alongside it).
Chapter 12 Curiosities
Businesses and Tarriffs
The cut-off date for posting to this forum is reached so you can no longer post to it.