Why is Capulet having a feast in Act 1, Scene 2 of Romeo and Juliet?
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Capulet has a feast in order to bring Juliet and Paris together. The feast is in the traditional form of a masquerade ball. In the beginning of Act II, Paris approaches Capulet and asks for Juliet's hand in marriage. Capulet thinks Juliet is too young at this point to be wed (after all, she has not yet turned 14). However, Capulet allows Paris to see Juliet at the feast/masquerade ball.
The purpose of the feast/masquerade is to introduce the two (Paris and Juliet). And, hopefully, begin a relationship which will blossom into marriage in two years time (when Juliet has turned 16). Capulet throws the feast/masquerade to accomplish the goal of introducing Paris and Juliet. However, Juliet meets Romeo at the feast/masquearde ball and, thus, begins the, "tale of woe," between, "Juliet and her Romeo."
I hope this helps! :)