Based on your understanding of gene regulation in the cell and the function of the trp operon, ...

If mutation occurs in the operator region the cell would no longer be able to metabolise tryptophan.

Due to alteration in the shape of tryptophan repressor protein, it would no longer be able to carry out its task which would ultimately call for the cell to continuously produce tryptophan on its own.

I'll provide more information since you asked via PM.

The lac operon is involved with the breakdown of lactose to use as a food source. The trp operon produces products that are used to manufacture an amino acid, tryptophan. The pathway controlled by the trp operon is an example of an anabolic pathway. The lac operon controls a catabolic pathway, one that breaks down complex molecules to release energy for biological work. The lac operon is controlled both by the abundance of its substrate, lactose, and by the abundance of glucose, an alternative to glucose. As there is no alternative to tryptophan the control of the trp operon is less complex than that of the lac operon.

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Thank you!!!