I’m Stuck - need to create an equation/model


New member
Jul 10, 2019
I need a model or equation to figure out a scenario.
“ We bill by the hour

“ We have three different billing rate tiers ($70, $112 and $210)

* The total budget we can bill is $500,000

* The average billing rate needs to be $109

* we have already billed hours in each tier so far this year, the model needs to take that number of hours already incurred within each tier

“ goal of the equation is to take all the above details into account (along with the current hours already incurred at each tier) to determine the minimum number of hours scenario that can exist. I know there are many different scenarios that can occur, but I’m after the one that has the smallest threshold of each tier that will collectively netbout the $500,000 budget at a blended/average rate of $109
Another way to summarize it is:
“Taking current hours/billing into account then projecting forward, what’s the minimum possible amount of hours within each billing tier for the remainder of the year, to hit the two requirements below?”
1) Bill $500,000 minimum
2) Achieve a blended rate of $109

I’m really stuck and would greatly appreciate help. If my instructions don’t make any sense: please advise and I’ll try to do better.

Subhotosh Khan

Super Moderator
Staff member
Jun 18, 2007
Have you thought through the following:
  1. Would you need one equation or multiple equations?

  2. What are the output/s of those equation/s?

  3. What are the input/s of those equation/s?

  4. Assign variable names to those inputs and outputs.
Please follow the rules posting in this forum. The rules are enunciated wt:

Please share your thoughts/work with us.


New member
Jul 10, 2019
Thank you so much for interest in helping!

1 - No restriction on number of equations.

2 - The output I need is the minimum number of hours in each billing rate tier it would take to collectively roll up to $500,000 in billing, yet the average hourly rate of the billing is $109 (this total hours capped at 4,587.

3 - inputs would be 1) currently known hours that have already occurred in each tier 2) billing rate of each tier which is also known.

4 - variable names (I’m far far far from a math expert, but this is what I’m thinking)
A = minimum hours of tier 1 rate of $210
B = minimum hours of tier 2 rate of $112
C = minimum hours of tier 3 rate of $70
I believe all other components are already known, but please advise if I’m thinking of it incorrectly.
- total billing can’t exceed $500,000
- average rate of the total hours billed can’t exceed $109 (thus I assume total hours can’t exceed 4,587
- the current number of hours in each tier is already known. But those hours do not add up to our maximum yet (hours and budget) we’re trying to figure out our minimum threshold for each “tier bucket” that needs to be met.

Please if any other questions don’t hesitate to ask.