To clarify the problem I will use a descriptive method...

There are 4 people working in a company, (Moe, Joe, Jack, John).
The amount of the job they are doing is $ 3,700. 
The deadline is in 7 days at a rate of 8 hours a day, the job will be
completed if all workers do their 56 hours in that week. (224 hrs in
total)

The pay they will get will be based on the amount of hours they spend
working on, but the problem is that some of them will be working more
hours than others, for instance:

Jack worked 80 hrs
Moe worked 50 hrs
John worked 90 hrs
Joe   worked 60 hrs
----Total-----280hrs

The problem is that there is a difference of 56 hrs extra (280-224) 

How can you get the right percentages for events like these where the
amount exceeds the number first given?

How can they have a fair share of the money based on the amount of hours worked?

Please describe the solution to this problem on how to obtain the
percentage and the amounts for each employee based on the hours
worked?

---

Request for Question Clarification by livioflores-ga on 02 Dec 2005 04:51 PST

I think that the problem can be managed in the normal way. You can
assume that the initial forecast for the hours worked failed due some
unexpected problems (this is very common in real life situations), so
to get a fair share of the money based on the amount of hours worked
just use the average weight of the hours worked by each worker:
Jack's percentage of hours worked = 100 * hours worked by Jack/280 =
                                  = 100 * 80/280 = 28.57%
Jack's Payment = 0.2857 * $3700 = $1057.09
etc.
Note: in this case the company assumes the loss of the opportunity
cost (the company lost the opportunity to use 56 hours of workers' job
to do other business).

The following is more tricky, but in very rare situations the company
can punish the team for the extra time delay, claiming an opportunity
cost loss. In this case a solution could be the following:
Each worker's percentage of hours worked is calculated in the same way
than in the first case.
Now calculate the opportunity cos for the company: 
For 224 hours of work they get $3700, then for 56 hours the proportional income is:
Op. Cost = $3700 * 56/224 = $925
This is the amount that the team must pay as mulct.

Now the total payment results in $3700 - $925 = $2775
Use the above amount to calculate the actual payment for each employee:
Jack's Payment = 0.2857 * $2775 = $792.82
etc.


Please let me know if this is the answer that are you looking for or
if I misunderstood the problem. In the first case I will claim the
prize by posting this in the answer box, in the second case I will
continue researching.

Regards,
livioflores-ga

---

Clarification of Question by oemoeniaoe-ga on 02 Dec 2005 07:33 PST

please specify the problem with the tricky solution... I understand
the first solution, but I want to obtain more information about how to
get the right amounts for the 2nd solution you gave me...
(3700-925 = 2775)

please complete the amounts for all four members, based on the 2nd
solution then you can caim the prize,

Thank you for your help...

Hi!!


Thank you so much for giving me the opportunity to answer your question.

In this case the company punished the team for the extra time delay,
claiming an opportunity cost loss (the company lost the opportunity to
use 56 hours of workers' job to do other business)..

In this situation the solution could be the following:
Each worker's percentage of hours worked is calculated based on the
amount of hours worked by him. To get the proportions just use the
average weight of the hours worked by each worker:
Jack's percentage of hours worked = 100 * hours worked by Jack/280 =
                                  = 100 * 80/280 = 28.57%

Moe's percentage of hours worked  = 100 * hours worked by Moe/280 =
                                  = 100 * 50/280 = 17.86%

John's percentage of hours worked = 100 * hours worked by John/280 =
                                  = 100 * 90/280 = 32.14%

Joe's percentage of hours worked  = 100 * hours worked by Joe/280 =
                                  = 100 * 60/280 = 21.43%



Now calculate the opportunity cos for the company: 
For 224 hours of work they get $3700, then for 56 hours the
proportional income (lost by the company due the delay) is:
Op. Cost = $3700 * 56/224 = $925
This is the amount that the team must pay as mulct.

Now the total net income for the team is: 
$3700 - $925 = $2775

Now we can use the above amount to calculate the actual payment for each employee:
Jack's Payment = 0.2857 * $2775 = $792.82
Moe's Payment = 0.1786 * $2775 = $495.62
John's Payment = 0.3214 * $2775 = $891.88
Joe's Payment = 0.2143 * $2775 = $594.68


I hope this helps you. Feel free to request for a clarification if you need it.

Regards,
livioflores-ga