## AMPL Session from Lecture 23, 11/05/2024



ampl: option solver gurobi;

% We solve the dual LP of the Farmer Jones LP directly
ampl: reset; model Dual_FarmerJones.txt; solve; display y1,y2,y3;
Gurobi 10.0.0: optimal solution; objective 370
4 simplex iterations
y1 = 0
y2 = 10
y3 = -10

% Ha! We had the original version. Let's change the coefficient of x2
% in the obj fn to 25 as being considered now.

ampl: reset; model Dual_FarmerJones.txt; solve; display y1,y2,y3;
Gurobi 10.0.0: optimal solution; objective 210
2 simplex iterations
y1 = 30
y2 = 0
y3 = 0

ampl: reset; model Dual_FarmerJones.txt; solve; display y1,y2,y3;
Gurobi 10.0.0: optimal solution; objective 210
2 simplex iterations
y1 = 30
y2 = 0
y3 = 0

% We had scaled the (min corn) constraint by 10. Let's go back to the
% original version (10x1 >= 30), and solve the dual LP again.

ampl: reset; model Dual_FarmerJones.txt; solve; display y1,y2,y3;
Gurobi 10.0.0: optimal solution; objective 370
2 simplex iterations
y1 = 0
y2 = 10
y3 = -1

% We get y3=-1, exactly as read off from the optimal primal tableau

% we use "display <ConstraintName>;" to display the corresponding
% optimal dual solution (after solving the primal LP)

ampl: reset; model FarmerJones.mod.txt; data FarmerJones.dat.txt; solve;
Gurobi 10.0.0: optimal solution; objective 370
2 simplex iterations
ampl: display x;
x [*] :=
 corn  3
wheat  2.8
;

ampl: display Land_Available, Labor_Hrs_Limit, Min_Crop_Limit;
Land_Available = 0
Labor_Hrs_Limit = 10

Min_Crop_Limit [*] :=
 corn  -1
wheat   0
;


% Note the shadow price of Min_Corn is -1. Indeed, if we increase the
% min_corn requirement from 30 to 31, the optimal revenue should go
% down by (-1)*1 = -1 dollar, as seen below

ampl: reset; model FarmerJones.mod.txt; data FarmerJones.dat.txt; solve; 
Gurobi 10.0.0: optimal solution; objective 369
2 simplex iterations
ampl: display x;
x [*] :=
 corn  3.1
wheat  2.76
;

ampl: