“ 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.