Final answer:
To break even, Brilliant Travel Agency needs to sell enough tickets to cover all costs, which can be calculated using the fixed costs and the variable costs per ticket. To make a target operating income of $12,000 per month, the number of tickets needed to be sold can be calculated by adding the target operating income to the fixed costs and dividing by the difference between the revenue per ticket and the variable costs per ticket.
Step-by-step explanation:
In order to calculate the number of tickets Brilliant Travel Agency needs to sell each month to break even, we need to determine the total costs and the contribution margin per ticket.
The total costs consist of the fixed costs and the variable costs per ticket. The contribution margin is the revenue per ticket minus the variable costs per ticket.
(a) To break even, Brilliant needs to sell enough tickets to cover the total costs. The total costs are the fixed costs plus the variable costs per ticket multiplied by the number of tickets to be sold:
Total costs = Fixed costs + (Variable costs per ticket x Number of tickets)
Setting the total costs equal to the revenue per ticket multiplied by the number of tickets will give us the break-even point:
Revenue per ticket x Number of tickets = Fixed costs + (Variable costs per ticket x Number of tickets)
Let's solve for the number of tickets:
Number of tickets = Fixed costs / (Revenue per ticket - Variable costs per ticket)
(b) To calculate the number of tickets Brilliant needs to sell in order to make a target operating income of $12,000 per month, we add the target operating income to the fixed costs:
Total costs = Fixed costs + Target operating income
Setting the total costs equal to the revenue per ticket multiplied by the number of tickets will give us the target operating income point:
Revenue per ticket x Number of tickets = Fixed costs + Target operating income
Let's solve for the number of tickets:
Number of tickets = (Fixed costs + Target operating income) / (Revenue per ticket - Variable costs per ticket)