AEB 6933
 Spring 1995
 Exercise FA4

 Factor x Factor

So far we have analyzed this data set by finding responses to
phosphorus for set levels of nitrogen (FA1, FA2, FA3-1 and FA3-2) or
by finding responses to nitrogen for set levels of phosphorus (FA3-3).
By doing this, it is possible to answer questions such as, "If I apply
25 kg ha-1 of P205, how much nitrogen should I apply?" But it does not
answer the question of how much of each amendment is best. To do this
requires the analysis of nitrogen and phosphorus simultaneously.

1. To obtain a first estimate of the nature of the 3-dimensional
surface (shown in two dimensions) construct a graph with nitrogen on
the vertical (Y) axis and phosphorus on the horizontal. (X) axis. Use
the values from the experiment as shown in the table in Exercise FA1.
Then using the averages from each treatment, write the corresponding
yields for each N-P combination at the intersection in the graph. For
example, the value for 0-0 (N-P) is 2210 and for 50-25 is 3880.
Follow the visiographic procedure from Hildebrand and Poey, pp. 108-
113.

2. Draw in iso-quant contours for 2500, 3000, 3500, etc.

3. Using the prices from Exercise FA3, draw in the iso-cost contours
and the expansion path.


4. Interpret your work.