How does availability of substrates and enzymes affect rate of reaction

Enzymes have an active site with a specific shape for binding to a specific substrate with the complimentary shape to enable reactions to occur. Initially when substrates are added the rate of a reactions increases,hence substrate concentration is said to be limiting. As substrates are added, the active sites on the enzyme become increasingly occupied, reducing the availability for the added substrates so the reaction rate decreases and enzyme concentration is said to be limiting. The reaction rate plateaus as all active sites are full so increasing substrate concentration further does not speed up reaction rate unless more enzymes are added.