Final answer:
The lac operon is most active when lactose is present and glucose is absent, allowing for maximal transcription of lactose metabolism genes.
Step-by-step explanation:
The lac operon is most active under conditions where lactose is present and glucose is absent. This scenario allows for the transcription of genes necessary for the metabolism of lactose. When glucose levels are low, cAMP accumulates, which binds to the catabolite activator protein (CAP). This cAMP-CAP complex then binds to the promoter region of the lac operon, enhancing RNA polymerase's ability to initiate transcription. Concurrently, lactose or its isomer allolactose acts as an inducer by binding to the lac repressor, altering its shape and preventing it from binding to the lac operator. This double mechanism of action—depletion of glucose increasing CAP binding, and presence of lactose removing the repressor—leads to the maximal expression of the lac operon, enabling the cells to efficiently utilize lactose as an energy source instead of glucose.