I wrote just a second ago:

> For more of a curved calculation, so that those that miss very few hours are
>  rewarded more than those that miss a great deal, a simple exponential (in
>  this case, a square) will work:
>
>            bonus = 1500 - k * h^2
>
>  where k = sqr (1000/(160)^2), which is 0.1976423538. Other exponentional
>  powers will modify the shape of the curve more or less steeply, but are as
>  easily calculated. As above, an IF statement is still required because the
>  conditions have the 160 hour discontinuity in them.

One of Efren's criteria that I didn't include in this calculation (in part
because it was only mentioned in his first posting) is the total bonus
requirement of $75,000.  That too can be easily accomodated, but it has to be
done by iteration, in the manner of Newtonian approximation (the manner by
which Newton solved square roots). The method is simple enough to explain:
guess -- and then guess again, walking your way back and forth until you have
an answer that is sufficiently accurate.

If a limit criterion is to be imposed, the exponential method associated with
the equation above has to be used.

We know the limits of the allowable guessing range. If everyone is to receive
a maximum bonus of $1500, the total bonuses delivered will be $120,000. If
everyone receives the minimum, the delievered bonuses will be $40,000. What
we don't know is the distribution of the hours missed, but Efren does (it's
in his database), and that can easily be programmed up using the formula:

   total bonus = sum of (1500 - k * h(i) ^ n), for all i = individual
employees

where n is the current guess for the value of the exponential, k =
(1000/(160)^n)^1/n, and h the number of hours missed. If the total bonus is
too large, then n needs to be increased (the steepness of the curve is
increased). Similarly, if the total bonus is less than $75K, then n needs to
be decreased (the curve needs to be flattened, or even perhaps bowed
negatively by exponents less than 1). By iterative approximation, you will
quickly walk your way into an exact solution so that the monies distributed
will be precisely $75,000.

Wirt Atmar