inat the beginning of act 2 ,there is a great sense of hope in the play. what are the 3 things that give both lomans and the audience hope

The second act begins with a dramatic shift in tone from the previous act, as Willy now appears cheerful and optimistic. Most importantly, the pipe connected to the gas heater with which Willy tried to commit suicide is now gone; Linda automatically assumes that Willy took it away himself, although this will come into question later in the play. Linda says that it was thrilling to see the boys leaving together, and says that Biff had a new, hopeful attitude. Willy dreams about buying a little place in the country.

But the sense of optimism that dominates the start of the act is somewhat unfounded. His change in mood is entirely based on Biff's meeting with Bill Oliver, trumped up in Willy's mind to a sure-bet business plan. Willy has gone from suicidal to confident and cheerful in the matter of one night, despite the fact that nothing concrete has been resolved, because the dream of the Oliver plan gave him hope.