Question

"A nightclub has fixed monthly costs of ​£6,428. During a typical​ month, 2,086 customers visit the​ nightclub, paying an average of ​£ 41 each. The​ club's variable costs average ​£13 per customer.

​
1. What is the​ break-even number of customers per​ month?
a) 134 customers
b) 362 customers
c) 512 customers
d) 928 customers
2. How much profit or loss is made from the 2,086 ​customers?
a) £19,144 profit
b) £23,752 profit
c) £29,068 loss
d) £36,234 loss''

Answer 1

The break-even number of customers per month for the nightclub is 362, making option (b) correct. The profit made from 2,086 customers is £19,144, which means option (a) is the correct answer for the second question.

Step-by-step explanation:

The student has asked for assistance with a problem relating to break-even analysis and profit calculation for a nightclub. To determine the break-even number of customers and the profit or loss made from 2,086 customers, one must understand the basic concepts of fixed and variable costs.

First, the break-even point is determined by the formula:

Break-Even Point (in customers) = Fixed Costs / (Price per Customer - Variable Cost per Customer)

For the given scenario:

Fixed Costs = £6,428

Average Revenue per Customer = £41

Variable Costs per Customer = £13

Hence, the break-even point in customers = £6,428 / (£41 - £13) = 362 customers. Option (b) is the correct answer.

To calculate the profit or loss, we use the formula:

Total Profit (or Loss) = (Average Revenue per Customer * Total number of Customers) - (Total Fixed Costs + (Variable Cost per Customer * Total number of Customers))

Total Profit (or Loss) for 2,086 customers: = (£41 * 2,086) - (£6,428 + (£13 * 2,086))

When we do the calculations, the result is a total profit of £19,144. Therefore, option (a) is the correct answer for the second part of the question.