order of adjective and noun

生活奢侈 is a noun phrase favored by Classical Chinese because remember in the old old days, writing is on bamboo slips with a "chisel".  Brevity and conciseness are the order of the day.  Words can be omitted when clarity is not affected.  Just like in English, headlines are not in perfect sentences.  Modern Chinese which is descended from Classical Chinese still retains many of older grammar structures.

From a translation angle, 生活奢侈 should not be translated as "Life is luxurious" but rather "luxurious life".  The subtle nuance in meaning is the same in both English and Chinese.

Hi Arash,

Think of 生活奢侈 (to live in Luxury) as a set phrase. It is perfectly acceptable to say 這個人過得一個過於奢侈的生活, which is in line with the rules of Chinese grammar you mentioned. 

奢侈品 (luxury item) uses the normal word order for Chinese. 

Laurence 

order of adjective and noun

Like Laurence said, 生活奢侈 is a set phrase, and the order is noun +adj,  e.g. 他生活奢侈。奢侈 is a adj, we can say: 他生活很奢侈 or 他不奢侈~。

Another “是” is a judge verb, we can say, but rarely use that: 他生活 是奢侈。And in the behind we always add another contrast sentence, like :他生活是奢侈，但是他习惯很好。

Last 奢侈品 is a none, we can say:  LV 是奢侈品。 

Hope it is useful for your learning.  Have a good day!