Problem: The business manager of an orchestra performs two Saturday evenings each month with a new program for performance. It incurs the following costs for each performance:
Fixed overhead costs $1,500
Rehearsal costs $4,800
Performance costs $2,200
Variable costs $1 per person
The Orchestra's business manager is concerned with profit. The profit margin is currently very thin and she would like to increase it. Tickets for the performances sell for $11 each and the usual attendance is 900 patrons.
The business manager is considering three options:
1. A "student rush" ticket price at $3 and sold to college students 1/2 hour before performance. She figures that she could get 200 students who normally would not attend the performances. Clearly, however, the price of these tickets would not cover even half of the average cost per ticket.
2. A Sunday matinee repeat of the Saturday evening perfomance with tickets prices a $7. The manager expects to sell 700 tickets but 150 of those people would have attended the higher priced Saturday performance. The net patronage would increase by 550 but the price of the ticket is, once again, less than the average cost per ticket.
3. A new series of concerts to be performed on the alternate Saturdays. The tickets would still be priced at $11. The expectation is that 800 tickets would be sold but that 100 of those would be to individuals who would have attended the old series instead of the new one. The new patronage would increase by 700.
Which option do you recommend as best to optimize profit and why. Is there more than one solution for increasing profit? Show your analysis for each option.