Where are the lipids and proteins constituting the cell membrane synthesized?

         
                    Where Lipids and Proteins are Synthesized
             The living cell has cell organelles that play vital physiologic functions in the cell. The cell membrane is made up of both lipid and proteins which play a vital role in cellular physiology. Protein synthesis in any given cell is performed by a cell organelle known as the ribosome. This ribosomes are attached to the rough endoplasmic reticulum. A physiologic process called the central dogma of a cell plays a vital role. It involves transcription of DNA to mRNA which contains the codes of the particular protein to be synthesized.
             This proteins are then either functional or structural depending on what they are designed to perform. The mosaic in the cell membrane containing phospholipids are formed by this proteins. The phospholipid layer contains the lipids which are manufactured at the smooth endoplasmic reticulum. An important point is to note that the smooth endoplasmic reticulum does not have the ribosomes hence this could explain its function towards the synthesis of lipids.
             The Golgi apparatus or bodies are the cell organelles responsible for production of cell secretions and modifications of this lipids before they reach their target sites. A physiologic process known as post-translational modification takes place in the Golgi apparatus. Note that the process of transcription generates mRNA which is then translated to proteins. The proteins and lipids that have been synthesized are then transported in membrane-bound vesicles. They then fuse with the cell membrane and the orientation depends on solubility. The alignment is based on the interaction with the cell and depends on whether a protein or lipid is hydrophilic or hydrophobic.
Reference
Linda Constanzo physiology 20th edition

Lipids and proteins are synthesized on the endoplasmic reticulum. Ribosomes are the site for protein synthesis. The ribosomes attached to the rough endoplasmic reticulum (rough ER) synthesize proteins. Those proteins are then used to form the mosaic in the phospholipid bilayer of the plasma membrane. Smooth endoplasmic reticulum (smooth ER) helps in the manufacture of lipids, which are important for cell functioning. Modifications take place in the golgi apparatus before they are sent to their destination. The golgi apparatus serves as an assembly line in which membrane proteins undergo post-translational modification. The synthesized membrane lipids and proteins must be transported by membrane-bound vesicles. The proteins and lipids made will then fuse with the cell membrane and orient themselves through hydrophobic and hydrophilic interaction within the cell.