Figure 2. Optimal Size, Number, and Location of Center Pivot Irrigation Systems for a Hypothetical
Irregularly Shaped Field.
b) Two Iorge sized pivots
and one smoll pivot
World peanut price was varied within the
relevant historic range (United Nations) to
illustrate the possibility of irrigating peanuts
sold at the world price. Two large center
pivots were selected by the model when the
world price was raised to 22 cents per pound
and using a land rental value of S40 per acre.
A larger peanut quota clearly results in
more irrigation and less land rental, Table 3.
As the peanut quota increases, production of
peanuts at the world price is reduced. World
price was increased to 18 cents and 22 cents
for 2,400 poundage quota as was done with
the 2,100 poundage quota. No peanuts were
produced at the world price at the higher
quota level. If marginal price exceeds break-
even price for a particular pivot size, a larger
quota will result in more irrigated acreage.
Even with a marginal price in excess of break-
even for the intermediate sized pivot, in-
creased quota will not result in positioning
an intermediate sized pivot.
The interrelationship between engineering
and economic considerations is clearly dem-
onstrated. First, price must sufficiently ex-
ceed breakeven for a particular sized pivot
and, second, the shape and size of the field
168
must allow appropriate positioning of that
particular sized pivot.
Figure 2 illustrates the optimal sizes and
locations for center pivots using the grid
system in Figure 1 and cost and return data
in Table 1. When the marginal price exceeds
21 cents, two large pivots are selected and
can be located in multiple positions in the
field. The small pivot in conjunction with
the two large pivots will be employed if
marginal price of peanuts exceeds 25 cents.
The intermediate pivot does not appear in
the solution because of field size and shape.
SUMMARY AND CONCLUSIONS
Irrigation in humid areas is used to sup-
plement water availability from rainfall, thus
providing protection from droughts that fre-
quently occur in crucial stages of the plant
growing cycle. The small and irregularly
shaped fields that are often found in the
Southeast have hindered the adoption of ef-
ficient high technology center pivot irriga-
tion systems. The mixed integer linear
programming model presented in this paper