Question

A bicycle store costs $2400 per month to operate. The store pays an average of $60 per bicycle that is sold in the shop. The average selling price of each bicycle is $120. How many bicycles must the store sell each month to break even?

a 39
b 40
c 41
d 42

Answer 1

The bicycle store must sell 40 bicycles each month to break even. This amounts to covering $2400 in fixed costs plus $60 per bicycle in variable costs with $120 revenue per bicycle sold.

Step-by-step explanation:

To calculate the break-even point for the bicycle store, we need to find the point where total costs equal total revenues. The fixed costs are $2400 per month, and variable costs are $60 per bicycle. The selling price per bicycle is $120. The break-even point occurs when the cost of operating the store plus the cost of the bicycles sold equals the revenue from selling bicycles.

The cost function is: C(x) = 2400 + 60x, where x is the number of bicycles sold. The revenue function is: R(x) = 120x. To find the break-even point, we set the cost equal to the revenue:

• 2400 + 60x = 120x
• 120x - 60x = 2400
• 60x = 2400
• x = 2400 / 60
• x = 40

Therefore, the store must sell 40 bicycles each month to break even. So, the correct answer is b) 40.