The correct answer is option 3: Proteins in mammalian cells are synthesized in the rough endoplasmic reticulum (ER).

Option 1 is incorrect. Proteins are not synthesized in the cell membrane. The cell membrane primarily functions as a barrier and a gatekeeper for regulating what enters and exits the cell.

Option 2 is incorrect. While proteins, in the form of amino acids, are obtained from food, they are not directly absorbed into mammalian cells. Proteins need to be synthesized within the cells.

Option 3 is correct. The rough endoplasmic reticulum (ER) is a membrane-bound organelle that is studded with ribosomes. These ribosomes are responsible for protein synthesis in the cell. The newly synthesized proteins are then transported through the ER to undergo further processing and modification.

Option 4 is incorrect. The Golgi apparatus is another organelle involved in protein processing and modification but not the site of protein synthesis.

In conclusion, proteins in mammalian cells are synthesized in the rough endoplasmic reticulum, making option 3 the correct answer.