Answer:

In Shakespeare's play "Twelfth Night," Sir Andrew Aguecheek is portrayed as a rather foolish and easily influenced character. He becomes infatuated with Olivia for several reasons:

1. Olivia's Beauty: Olivia is described as a beautiful and wealthy noblewoman. Her physical beauty and social status make her an attractive prospect for many suitors, including Sir Andrew.

2. Social Pressure: Sir Andrew is encouraged to pursue Olivia by his friend, Sir Toby Belch, who hopes to benefit from Olivia's hospitality and generosity if she marries Sir Andrew.

3. Gullibility: Sir Andrew is gullible and easily manipulated by those around him. He may genuinely believe that Olivia loves him or could love him, even though she has not shown any real interest in him.

4. Lack of Self-Awareness: Sir Andrew lacks self-awareness and is not particularly perceptive. He might not fully grasp Olivia's disinterest or her feelings for another character, Cesario (who is actually Viola in disguise).

Overall, Sir Andrew Aguecheek's infatuation with Olivia is largely driven by his own naivety, the influence of others, and Olivia's social standing and beauty. However, his pursuit of her love is one of the humorous subplots in the play, as it highlights the theme of unrequited love and the absurdity of some of the characters' actions.