For many enzymes, the rate of product formation increases as the concentration of the substrate increases. eventually the rate of the reaction reaches a maximum at which further increases in the concentration of the substrate have no effect.

The statement is true.

Increasing the substrate concentration increases the rate of reaction because all of the enzyme molecules are able to act on substrate molecules, and none of the molecules remain idle. However, because the number of enzyme molecules is limited, there comes a point where the substrate is so far in excess that each substrate molecule has to "wait for its turn" to be acted upon by the limited enzyme molecules. Therefore, the rate of reaction reaches a maximum value and remains constant.