The given question asserts two statements about Chikmagalur and Mandya, two regions in India. Each option represents a possible combination of these assertions being correct.

Option 1, `1 only` suggests that Chikmagalur is well-known for sugar production, which is incorrect. Chikmagalur is rather famous for coffee production, not sugar.

Option 2, `2 only` states that Mandya is well-known as a coffee-producing region, which is also incorrect. Mandya is actually renowned for the cultivation of sugarcane, not coffee.

Option 3, `Both 1 and 2` implies that both statements are correct, which they are not, based on the explanations provided above.

Option 4, `Neither 1 nor 2` says that neither of the statements is correct, which is indeed the case. Chikmagalur is a coffee-producing region and Mandya is known for its sugar production, contradicting the original assertions. Thus, answer 4 is the correct answer.