These yield response plots have the incorrect  independent variable I suspect.  Think about a 3-axis surface plot: APH, Yield, and Population.  When thinking of your population target, you want Pop versus APH, not yield versus pop.   "FieldScript" is making you pay for something that is already known to you/us.  In fact - you are paying them to generate/verify the surface response curve on these three dimensions - though I highly doubt is is any better than the response curve I have below.  They have provided no proof that they are making you any money.   Use this equation and save thousands. 

 I would NOT use the variety specific population curves for much of anything.   I would rather use the aggregate equation below for any population selection  (maybe consider tweaking this to fit specialized hybrid performance if data is known - though Monsanto is now holding this data close to their chest). 

Pioneer did a meta-analysis of multiple years data, first in the early 2000's, then recently published them again around 2010.  I have interpreted the maximal economic ROI to be just left of the yield response maxima.   Since I do not have the original data, I must approximate a bit. 

See here for the latter study: 
https://www.pioneer.com/home/site/us/agronomy/library/template.CONTENT/guid.9C26CEFA-2FB0-483D-1308-F02D23AB6293

I bet $100 no-one can prove a statically better way to prescribe ANY variety better than this relationship here:

http://talk.newagtalk.com/forums/thread-view.asp?tid=452947&mid=3675857#M3675857

NOTE:  X-axis is the soil (or grid's) expected APH. - i.e. the independent variable.   The Y-axis is the target corn stand pop. 

Use either the 4th order or second order fit (piece-wise /sigmoidal relationship would be better).  The minimum value is near 18,000 due to the effect of shading (and weed pressures) being limited below 16-18,000.

EDIT:  Please note, this equations is for APH less than about 250 bu/acre.  Anything above that is either untested (or under tested) or anecdotal.   I suppose an APH might do well at 38,000 - 42,000, but I just don't have published data to show that.  Mr. Stine advocates this.   I have grown 250 bushel corn on 33,000 plants with the right amount of rain. 

Pictured here below (and attached) is the data from which I built the equation.  Points below 150 are from other studies (dryland corn population response rates).    Please follow the link above to see my excel sheet and fitted equations. 

(chart_yield_resp_plant_pop.gif)

chart_yield_resp_plant_pop.gif (20KB - 187 downloads)