Table 2. Illustration of a Linear Programming Matrix Used to Determine the Optimal Number, Location and Size of Center Pγvot Irrigation Systems
|
Item" |
Decision variables |
Constraint | ||||||||||
|
Pivot 1 |
Pivot 2 |
Pivot 3 |
...W2,5 ...W3,3 W3,4 |
W3,5 |
W3,6 W3,7 ...W4,3 W4,4 W4,5 |
W4,6 W4,7. Selll |
Sel 12 |
Sel 13 |
Rent |
Dry | ||
|
Objective ..... |
~. ^A |
-B |
-C |
Pl |
P2 |
P3 |
R |
-K | ||||
|
Pivot 5,5 ...... |
1 |
1 |
1 |
≤1 | ||||||||
|
G2,5 ............ |
1 |
-1 |
≤1 | |||||||||
|
G3,3 ............ |
1 |
-1 |
≤1 | |||||||||
|
G3,4 ............ |
1 |
-1 |
≤1 | |||||||||
|
G3,5 ............ |
1 |
1 |
-1 |
≤1 | ||||||||
|
G3,6 ............ |
1 |
-1 |
≤1 | |||||||||
|
G3,7 ............ |
1 |
≤1 | ||||||||||
|
G5,2 ............ |
1 |
≤1 | ||||||||||
|
G5,3 ............ |
1 |
1 |
≤1 | |||||||||
|
G5,4 ............ |
1 |
I |
1 |
≤1 | ||||||||
|
G5,5 ............ |
1 |
1 |
1 |
≤1 | ||||||||
|
G5,6 ............ |
1 |
1 |
1 |
≤1 | ||||||||
|
G5,7 ............ |
1 |
1 |
≤1 | |||||||||
|
G5,8 ............ |
1 |
≤1 | ||||||||||
|
G8,5 ............ |
1 |
≤1 | ||||||||||
|
Yield ............ |
D |
E |
F |
-H -H -H |
-H |
-H -H -H -H -H |
-H -H -1 |
-1 |
-1 |
V |
=0 | |
|
Land ............. |
X |
Y |
Z |
1 |
1 |
≤L | ||||||
|
Quota........... |
1 |
≤Q1 | ||||||||||
|
Contract ....... |
1 |
_≤Qz | ||||||||||
• Alphabetic characters in the matrix represent specific coefficients used in the analysis: A, B, and C are the annual costs of each size of center pivot system (including
peanut production costs); D, E, and F are the total yields of peanuts that would be expected from the land covered by each pivot; H is the irrigated yield increase for
each grid area; K is the cost∕acre of поп-irrigated peanuts; L is the total land available; Pl, P2, and P3 are the quota, contract, and world prices for peanuts, respectively;
Q∣ is the quota available for the field being considered; Q2 is the total that can be sold at contract price; R is the rent per acre; V is the yield per acre for non-irrigated
peanuts; and X, Y, and Z are the acres covered by each pivot irrigation system.
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