In Twelfth Night, how did Olivia treat Duke Orsino, and what was the duke's attitude toward her?

Duke Orsino is madly in love with Lady Olivia and opens the play by expressing his deep love for her, which encompasses his entire being and distracts him from his everyday duties. Duke Orinso ends up sending Viola, disguised as a young male named Cesario, to woo Lady Olivia for him. Ironically, Lady Olivia has no interest in returning the duke's love and falls for Cesario. She continually rebuffs Duke Orsino's advances and even uses her brother's death as an excuse to avoid him. She is determined to win Cesario's heart and even gives "him" a ring.
Despite Lady Olivia's lack of interest and unrequited love, Duke Orsino continues to strive for her love by sending Cesario back to her with a jewel. Unfortunately, Lady Olivia continues to dismiss his advances and focus on Cesario, who is actually a woman. Despite Lady Olivia's unrequited love, the duke is persistent and continues making advances in hopes of winning her heart.