Question

John manages a Symphony Orchestra with one Saturday evening performance per week . The hall has a capacity of 1,100 patrons per performance . The price per ticket is $ 10 . The symphony hall has a weekly fixed rental cost of $ 1,500 . The per performance costs are as follows : Rehearsal Costs ( one for every series ) $ 4,500 Costs per performance $ 2,000 Cost of program and tickets $ 1 per patron Recent attendance at the symphonies has been 900 patrons , which has resulted in a per performance profit of $ 100 . John is considering three proposals to increase profits by " reaching out " to new markets : 1 . A student ticket priced at $ 4 sold to college students 30 minutes before each performance on a first come , first serve basis . Management estimates that it could sell 200 tickets for each performance to people who would otherwise not attend . 2 . A matinee repeat of the Saturday evening performance with tickets priced at $ 6 . Management estimates that it could sell 700 tickets for each matinee performance but 150 of those would be purchased by patrons who would otherwise have attended the Saturday evening show . 3 . A new series of concerts to be performed on Sunday with tickets priced at $ 10 . There will be two performances per week : the regular and the new series . Management estimates that it could sell 800 tickets per show but 100 would be purchased by patrons who would otherwise have attended the regular Saturday performance . Question: What is the total weekly profit considering each proposal ? Which proposal should John consider implementing ?

Answer 1

John must calculate profit by considering additional revenue and subtracting cannibalized sales and extra costs for each proposal. Proposal 1 results in an additional $800 in revenue.

Step-by-step explanation:

When assessing how to maximize revenue from a symphony orchestra with limited seating capacity and performances, John has to consider the fixed costs of staging performances and variable costs per patron.

As well as the demand elasticity for concert tickets at different price points. To evaluate which of the three proposals would yield the highest total weekly profit, we need to calculate the profit from each scenario.

For proposal 1, by selling 200 student tickets at $4 each, revenue from student tickets would be $800. Since these tickets are sold to those who would otherwise not attend, we add this to the existing profit of $100. Total profit for proposal 1 is $900.

Proposal 2 involves a matinee with 700 tickets at $6 each, which is $4,200 in revenue. However, since 150 tickets would cannibalize the evening show, we subtract $1,500 (150 tickets at $10) from the revenue.

Additionally, there are extra costs such as rehearsal and costs per performance to consider. The total profit for proposal 2 would be calculated by subtracting these figures from $4,200.

Proposal 3 introduces a Sunday series with 800 tickets at $10 each, totaling $8,000 in revenue. Subtracting the 100 tickets that would be lost from the Saturday show ($1,000), and including the additional fixed and variable costs, provides the total profit for proposal 3.

John needs to compare the profits from each proposal after accounting for costs to determine which option would bring the most financial benefit to the symphony hall, keeping in mind that setting ticket prices can affect both the volume of ticket sales and the overall revenue.