percent among sizes. Additional production
costs were estimated as $.027 per pound and
were invariant with respect to system size.
The variation in breakeven price for the three
pivot sizes was largely a result of economies
of size in ownership costs.
Table 2 illustrates an abbreviated matrix
of the form used to solve the problem. Integer
(0-1) decision variables are included which
illustrate locating a center pivot at point 5,5
which is one of many possible locations il-
lustrated in Figure 1. The complete model
included variables for all feasible locations.
Pivot 1 is the smallest system considered and
would cover only five grid areas; 4,5; 5,4;
5,5; 5,6; and 6,5. Obviously, larger systems
would cover more grid areas—the interme-
diate size covers 13 and the largest size covers
29 grid areas.
The “W” decision variables account for
any overwatering that might occur if center
pivots should overlap in the field. The “Sell”
activities represent selling peanuts at quota,
contract, and world prices, respectively. The
“Rent” activity permits land to be rented out
and the “Dry” activity permits the produc-
tion of поп-irrigated peanuts.
RESULTS
Dependent upon quota poundage and the
contract selected, the marginal price re-
ceived will be either the quota price, con-
tract price for non-quota peanuts, or world
price. Profit resulting from this price is de-
termined for dry and irrigated peanuts and
compared to the rental value or land value
in its best alternative enterprise. If irrigated
peanuts are the most profitable of the three
alternatives, the grid system technique will
select the optimal size and location for center
pivots. The model follows existing peanut
marketing practices by first selling as much
as possible at the quota price. After the quota
level is completely filled, peanuts are sold
at the contract non-quota price and finally,
any additional peanuts are sold at the world
price. This procedure in effect negates con-
sideration of the peanut prices as blended
prices.
In a more simplistic farm management en-
terprise selection linear programming model,
the conditions for inclusion of an enterprise
in the optimal solution could be developed
in a rather straightforward comparison of rel-
ative profitability. The points of indifference
between pairs of enterprises would be rep-
resented mathematically as:
(7) (P-C) Y, = R;
(8) (P-C) Y1 = (P-C) Yd; and
(9) (P-C) Yd = R;
where:
P = marginal price of peanuts;
C = cost per unit of peanut production;
Y = yield (I = irrigated; D = dry); and
R = rental value.
The model would choose irrigated peanuts
over land rental (eq. 7), if the irrigated pea-
nut profit margin times the irrigated yield
exceeded rental value. Irrigated peanuts
would be included instead of dry production
(eq. 8), if the irrigated profit margin times
irrigated yield were greater than dry profit
margin times dry yield. Dry peanut produc-
tion would be selected in the place of rental
acreage (eq. 9), if the dry profit margin times
dry yield exceeded rental value.
The peanut poundage quota system and
engineering considerations concerning field
size and shape complicate the relative prof-
itability conditions (equations (7)-(9)).
These conditions are still relevant but must
be interpreted carefully. Under the quota
system, the price of the last peanut sold is
the appropriate price to use for relative prof-
itability calculations. Thus, a marginal price
is being used.
On first inspection, it might be concluded
from equation (7) that a higher land rental
value will necessarily decrease irrigated pea-
nut acreage. However, increased land rental
acreage will reduce acreage available to ful-
fill the peanut quota and can thereby change
the marginal price.
In addition, the conditions might suggest
the greater relative profitability of irrigation
with a certain pivot size, but field size and
shape may not allow positioning of the pivot
without excessive overlap. This possibility is
illustrated in Figure 2 by the absence of the
intermediate sized pivot even though its rel-
ative profitability is clearly higher than the
small sized pivot.
As would be expected, when the value of
land rental alternatives increase, land rental
acreage increases. Also, higher rental values
result in a higher marginal price at which
peanuts would be produced with more ir-
rigated acreage. Thus, the existence of higher
valued alternative crops causes irrigation and
the more intensive use of land to be more
profitable.
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