Question

You are the sole proprietor (single owner & employee) of a home cleaning business. You have two ways to clean homes: using (a) broom or (b) Roomba®. You charge the customer $150 to clean a home, but the costs are different as follows:

Broom

Fixed cost $20.00

Variable cost $75.00/home

Roomba

Fixed cost $1,250.00

Variable cost $20.00/home

What is the breakeven quantity after which using the Roomba becomes more cost-effective than using the broom?

Answer 1

Let the break-even quantity be Q omes

For using Broom:

Fixed Cost = $20.00

Variable Cost = $75.00/home

Cost of cleaning Q homes with broom = Fixed Cost + Q * Variable Cost per home = $20.00 + Q * $75.00 = $20 + $75Q

For using Roomba:

Fixed Cost = $1,250.00

Variable Cost = $20.00/home

Cost of cleaning Q homes with broom = Fixed Cost + Q * Variable Cost per home = $1,250.00 + Q * $20.00 = $1250 + $20Q

At break-even point,

Cost of cleaning homes using either Broom or Roomba is equal

=> $20 + $75Q = $1250 + $20Q

=> $75Q - $20Q = $1250 - $20

=> $55Q = $1230

=> Q = $1230/55 = 22.36

Therefore, the quantity after which using the Roomba becomes more cost-effective = 22.36 (Roomba would be be more cost-effective if the quantity is 23 homes or above.