I can't wrap my head around this one Math question for months...

Question

Hello,

I find it hard to wrap my head around Break Evens where there is a limit on one of the costs (example below):

“What’s the minimum number of customers/month needed to cover trainer + fixed cost, if:

Each trainer can handle 150 customers/month
Each trainer is paid $3,000/month
Fixed monthly cost (lease, marketing, admin) = $12,000/month
Contribution per customer (after all direct costs) = $30

I've seen variations where people calculate it in blocks (i.e. Profit per coach) or to just model the entire thing (i.e. are we breaking even with one coach, two coach...)

The most efficient way I found so far is to just make it into an equation with customers as 'x' and then number of trainers as x/150 * 3000 to find the number. In works in this question but for others, I'll get a decimal which makes me double check the entire thing and needing to adjust for 1-2 units of the final answer

This is a real MBB question there are just so many ways to solve it - none seem 80/20 or effective enough

Thank you !

Answer 1

The puzzling point here is "direct costs". It can be related to trainer costs, trainer+fixed costs, or costs that's not related to trainer and fixed one

Answer 2

Profit per trainer seems to be the right way, and only requires three steps.

(150 * $30) - $3000 =$1500 maximum profit per trainer per month

$12000 / $1500 = minimum 8 trainers needed to break even on a monthly basis

In our calc, we have assumed each of the 8 trainers is fully utilized: 8 * 150 =1,200 customers per month

Doing a trial and error approach (e.g., testing various numbers of trainers to narrow in on the right number) is inefficient and would be a red flag to an MBB interviewer.

Let me know if you need more help on this kind of question.

Answer 3

Hey!

You're on the right track! The best 80/20 way is to use your equation but round trainers up whenever you get a decimal.

So here:
Trainer cost = ($3,000 × ceil(x/150))
Total cost = $12,000 + trainer cost
Break-even: $30 × x = total cost

Just plug in values of x in steps of 150 until revenue ≥ cost. It’s fast, accurate, and avoids overthinking decimals.

Let me know if you want help with a shortcut sheet!

Best,
Alessa 😊

Answer 4

Hi there,

I see you've received great answers on this already.

If you're doing case prep, I'm sharing here a resource that you might find useful:

Cheatsheet: The Must-Know Consulting Terms for Interviews

Best,
Cristian