The next winner of America’s Idol will perform at your fraternity’s charity event for free at your school’s basketball arena (25,000-person capacity) on January 28, 2011. The school is charging your fraternity $37,500 for the facilities and $10 for each ticket sold. The fraternity asks you, their only numbers-astute member, to determine how much to charge for each ticket. The group wants to make a profit of $8 per ticket sold. You assume that 15,000 tickets will be sold.

a. What is the total cost incurred by the fraternity if 15,000 tickets are sold?

b. What price per ticket must be charged for the fraternity to earn its desired profit margin?

c. Suppose that on the morning of January 28, 2011, a major snowstorm hits your area, bringing in 36 inches of snow and ice. Only 5,000 tickets are sold because most students were going to buy their tickets at the door. What is the total profit or loss to the fraternity?

d. What assumptions did you make about your calculations that should have been conveyed to the fraternity?

e. Suppose instead that fair weather prevails and, by show time, 20,000 concert tickets are sold. What is the total profit or loss to the fraternity?