Rule 1: We often use much in negative sentences with uncountable nouns.
Sentence b: That isn't much time.
Rule 2: We often use many in negative sentences with plural countable nouns.
Sentence c: We haven't got many cartons of orange juice.
Rule 3: We use a lot of in affirmative and negative sentences with countable and uncountable nouns.
Sentence a: We've got a lot of bags of crisps.