In the example:


 bl = [(87.750)(4.875) (27.00)(13.0875)] / 60.75
 = 1.225

 b2 = -13.8375 / 60.75
 = -0.228

Now that bl and b2 are known, find the intercept a by
using the mean values of Y, X1, and X2 as follows:

 6.333 = a + 1.225(1.5) 0.228(3.75)

from which
 a = 5.350

Remembering that X1 is N and X2 is N2, the complete
equation is:

 Y = 5.350 + 1.225 N 0.228 N2

This is the same equation as was found by the visiographic
method, using the average values of the replications. The
values in this equation have been coded so the magnitude
of the numbers is different. Here N is measured in units
of 100 kg and Y in metric tons. Maximum production
results from N = 2.7 units (270 kg), and production at
this level is 6.99 tons (6990 kg). These are essentially
the same values found before.
 In order to find the level of N which maximizes
profit, use the prices for the same units in which N and
rice are measured. Because 1 kg of N costs $4.40, the
price of 100 kgs is $440. With rice at $2.80/kg the price
of a ton is $2800. In order to find the amount of N which
will maximize profit, calculate:

 dY/dN = 1.225 0.456 N = 440/2800
 so N = 2.34 units or 234 kg

 This is essentially the same value as was found by the
visiographic method. The difference is due to slight
roundoff error from coding.