the Parent Teacher Association $($PTA$)$ of Meadow High School is planning a fund$-$raising campaign. The PTA is considering the possibility of hiring Eric Logan, a world$-$renowned investment counselor, to address the public. Tickets would sell for $$29$ each. The school has agreed to let the PTA use Harville Auditorium at no cost$.$ Mr$.$ Logan is willing to accept one of two compensation arrangements. He will sign an agreement to receive a fixed fee of $$10,450$ regardless of the number of tickets sold. Alternatively, he will accept payment of $$19$ per ticket sold. In communities similar to that in which Meadow is located, Mr$.$ Logan has drawn an audience of approximately $550$ people.

b$-1.$ Assume the PTA pays Mr$.$ Logan a fixed fee of $$10,450.$ Determine the amount of net income that the PTA will earn if ticket sales are $20$ percent higher than expected. Calculate the percentage change in net income.

b$-2.$ Assume that the PTA pays Mr$.$ Logan a fixed fee of $$10,450.$ Determine the amount of net income that the PTA will earn if ticket sales are $20$ percent lower than expected. Calculate the percentage change in net income.

b$-3.$ Assume that the PTA pays Mr$.$ Logan $$19$ per ticket sold. Determine the amount of net income that the PTA will earn if ticket sales are $20$ percent higher than expected. Calculate the percentage change in net income.

b$-4.$ Assume that the PTA pays Mr$.$ Logan $$19$ per ticket sold. Determine the amount of net income that the PTA will earn if ticket sales are $20$ percent lower than expected. Calculate the percentage change in net income.