The social committee of a college’s student government is planning the annual graduation dinner and dance. The preferred band can be signed for $1000 plus 10% of ticket revenues. A hall can be rented for $4400. Fire regulations limit the hall to 400 guests plus the band and caterers. A food caterer has quoted a price of $24 per person for the dinner.
The committee thinks that the event will be a sellout if ticket prices are set at $46 per person. Some on the committee are in favour of less crowding at the dance and argue for a ticket price of $56. They estimate that 300 will attend at the higher price.
a. Calculate the number of tickets that need to be sold at each price to break even.
b. What will be the profit at the predicted sales for each ticket price?