Ticket price and discount for a profit target

A drama club hires a hall with \(120\) seats for one night. The hire charge is \(\$450\), and every ticket sold costs the club a further \(\$3.50\) for programmes and refreshments. Tickets are sold at \(\$12\) each.

1. Find the least number of tickets the club must sell to make a profit of at least \(\$300\).[3]
2. The club decides to give a discount of \(\$d\) on every ticket. Find the greatest value of \(d\) for which a full hall still gives a profit of at least \(\$300\).[3]
3. With the discount in (b), find the least number of tickets that must be sold to reach the target. Comment on how sensible this discount is.[2]
4. State one assumption about the club's costs or sales in this model, and check whether your answer to (a) is realistic for this hall.[2]