Question

Your new garage band wants to hold a concert at the end of the semester on the VU campus. You estimate that the expected crowd size will depend on ticket price (i.e., the lower you price the tickets the more people will show up). Specifically, the expected crowd size is normally distributed with a mean of 3000 – ticket price*100 and standard deviation 30% of the mean (minimum of 0). The average expenditure on concessions is also normally distributed with mean $10 and standard deviation of $4 (minimum of 0). The band's profit is 50% of sum of gate and concession sales minus a fixed cost of $10,000 paid to the university.

1. What is the probability that the band will achieve a positive profit when tickets are priced $7?
2. Develop and interpret a 90% confidence interval for the mean profit when tickets are priced $10 (using 5000 iterations).
3. What should you price tickets at to maximize expected profits? (consider values $5, $7, $9, $12, $15, and $18 per ticket).

**In Excel and using @Risk

Answer 1

Expected revenue of Band=3000*$7= $21000

Cost of Band= $10 (Concession)+ $10000 (fixed) = $ 10010

Profit Expected = $21000* 50%-$10010 = $490.