Although rarely seen in its kanji form, につき is a grammar pattern that comes from a combination of に and the conjunctive form of the う- Verb 就（つ）く ‘to take up (A)’, or ‘to assume (A)’. This meaning is usually in regard to assuming a new position, such as a new job.
However, the particular meaning conveyed here will be closer to ‘due to (A), (B)’, ‘on account of (A), (B)’, or ‘for each (A), (B)’. につき will follow nouns directly, before the (B) part of the sentence describes what is happening ‘due to’ or ‘on account of (A)’.

• 閉店（へいてん）につき、特別（とくべつ）セール開催中（かいさいちゅう）！
  Due to our store closing, there is a special sale going on!
• 工事（こうじ）中（ちゅう）につき、この先（さき）立（た）ち入（い）り禁止（きんし）。
  Due to construction, entry beyond this point is prohibited.
• この商品（しょうひん）は大人気（だいにんき）のため、一人（ひとり）につき二（ふた）つまでとさせていただいております。
  Since this product is very popular, we are limiting this product to two per person.

This grammar point is quite formal, so it is often seen in formal documents, announcements, and notifications.
Regardless of the several common English translations, the base meaning of ‘to affix to (A)’ is kept in all of the uses of につき, as it simply implies that (B) is in answer to, exists in a way that is directly linked to, suitable for, or caused by (A).