Sliding Linear Scale

[john434]

Hi,

I have been passed an urgent piece of work that i just cannot fathom out on my own. It involves paying Practices on a sliding scale.

This is the guidence i have:

Lower threshold 20% = £196.07
Upper threshold 50% = £117.64

an average practice will receive £196.07 if the proportion of women identified is equal to or more than 50%. An average practice will receive £117.64 if the proportion is 20%. Any achievement between 20% and 50% will be paid out on a sliding linear scale e.g. if an average practice were to achieve 35% they will receive £156.86.

Since i have the figures for both the lower and upper thresholds, it must be simple to work out any value inbetween these. If it is, i can't see it for the life of me.

Thanks in advance

 

[AnotherHiggins]

To verify:

Lower threshold 20% = £196.07
Upper threshold 50% = £117.64

Those values are reversed, right?

OK, so your base is 117.64 with an additional 78.43 possible (196.07 - 117.64 = 78.43).

And you need to figure out where the clinic is between 20% and 50%, so that's 30% possible (50% - 20% = 30%).

And you'll pay out a portion of the $78.43 (on top of the base of 117.64) according to what percentage of the available 30% they achieve.

Base = 117.64
Bonus = 78.43
Upper = 50
Lower = 20
Clinic = 35

So for 35%, the logic would be:
[tab]=Base + (Bonus * ((Clinic-Lower) / (Upper-Lower)))
Or, removing superfluous parentheses and substituting in values:
[tab]=117.64 + 78.43 * (35-20) / (50-20) = 156.855

[tt][blue]-John[/blue][/tt]
[tab][red]The plural of anecdote is not data[/red]

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[NWBeaver]

To add to what John posted, here's the algebra lesson involved in your problem...

A linear problem like this can be solved with an equation of the form...

y = mx + b where m is the slope and b is the y intercept.

If you were to make a graph with the percentage on the x axis and the payment amount on the y axis, the slope m, of the line is then the rise over the run or (y2-y1)/(x2-x1), which in your case if we plug in the numbers becomes (196.07-117.64)/(50-20)=(78.43/30)

Using one of your data points, x=20, and y=117.64 we can solve for b...

b= 117.64 - (78.43/30) * 20 = 65.353

So the equation is then...

y = (78.43/30) * x + 65.353

where x is the percentage 20 to 50 and y is the payment .

 

[dallen43]

The above formula "=Base + (Bonus * ((Clinic-Lower) / (Upper-Lower)))" works as long as the clinic percentage is between 20 and 50. You need to add "if" conditions to handle less than 20 and more than 50 conditions.