## AMPL Session from Lecture 8, 09/12/2024

## Some additional comments have been added afterward for 
## increased readability.

ampl: option solver gubori;  # that's a typo! Should be gurobi!!
      	     	    	     # ampl would've thrown an error when
			     # asked to solve...

ampl: option solver gurobi;
ampl: model farmerJ.mod.txt;
ampl: data farmerJ.dat.txt;

## The files farmerJ.mod.txt and farmerJ.dat.txt are the versions that
## were written up live in class. On the web page, the cleaned up
## versions titled FarmerJones.mod.txt and FarmerJones.dat.txt are
## posted.


ampl: reset;
## 'reset' clears out both model and data from the ampl session
   

ampl: model farmerJ.mod.txt; data farmerJ.dat.txt;

## The 'expand' command writes out, i.e., expands, the objective
## function or constraints

ampl: expand Total_Revenue;
maximize Total_Revenue:
	30*x['corn'] + 100*x['wheat'];

## You could expand multiple constraints together.

ampl: expand Land_Available, LaborHrsLimits, MinCropLimits;
subject to Land_Available:
	x['corn'] + x['wheat'] <= 7;

subject to LaborHrsLimits:
	4*x['corn'] + 10*x['wheat'] <= 40;

subject to MinCropLimits['corn']:
	10*x['corn'] >= 30;

subject to MinCropLimits['wheat']:
	25*x['wheat'] >= 0;


ampl: solve;
Gurobi 10.0.0: optimal solution; objective 370
2 simplex iterations

## 'display' can be used to print the values of any variables after
## solving the problem

ampl: display x;
x [*] :=
 corn  3
wheat  2.8
;

## 'display'ing a constraint lists it's dual or shadow price - more on
## this topic later on.

ampl: display LaborHrsLimits;
LaborHrsLimits = 10

ampl: display Total_Revenue;
Total_Revenue = 370

ampl: reset; model n_farmerJ.mod.txt;
ampl: reset; model n_farmerJ.mod.txt; data n_farmerJ.dat.txt;
ampl: solve; display x;
Gurobi 10.0.0: optimal solution; objective 370
2 simplex iterations
x [*] :=
1  3
2  2.8
;

ampl: display MinCrop;
MinCrop [*] :=
1  30
2   0
;

ampl: display MinCrop[2];
MinCrop[2] = 0

## We could use the 'let' command to reassign one (or more) parameter
## values. This is a convenient way to make such small changes without
## 'reset'-ing the whole data file.

ampl: let MinCrop[2] := 10;
ampl: display MinCrop;
MinCrop [*] :=
1  30
2  10
;

ampl: solve; display x;
Gurobi 10.0.0: optimal solution; objective 370
0 simplex iterations
x [*] :=
1  3
2  2.8
;

ampl: let MinCrop[2] := 60;
ampl: solve; display x;
Gurobi 10.0.0: optimal solution; objective 370
0 simplex iterations
x [*] :=
1  3
2  2.8
;

## Since Jones is already making 25*2.8 = 70 bushels of wheat, the
## optimal solution remains the same. But now let's try to set the
## minimnum corn requirement up to 40 bushels/week.

ampl: let MinCrop[1] := 40;
ampl: solve; display x;
Solution determined by presolve;
objective Total_Revenue = 360.
x [*] :=
1  4
2  2.4
;

## To make 40 bushels of corn, Jones has to farm corn in 4 acres, and
## hence the total revenue decreases to 360 since he cannot grow as
## much wheat as before any more.

ampl: reset;

## Again, Myinv.mod/dat.txt were created in real time in class. The
## cleaner versions (InvProb.mod/dat.txt) are posted on the course web
## page.

ampl: reset; model Myinv.mod.txt;
ampl: reset; model Myinv.mod.txt; data Myinv.dat.txt;
ampl: solve; 
Gurobi 10.0.0: unbounded problem
2 simplex iterations

suffix unbdd OUT;
ampl: reset; model Myinv.mod.txt; data Myinv.dat.txt; solve;
Gurobi 10.0.0: unbounded problem
2 simplex iterations

suffix unbdd OUT;
ampl: 
ampl: 
ampl: expand NetCost;
minimize NetCost:
	5*x[1] + 8*x[2] + 7*x[3] + 4*x[4] + 2*s[1] + 2*s[2] + 2*s[3] - 6*s[4];

ampl: expand InvBalance;
subject to InvBalance[1]:
	-x[1] - s[0] + s[1] = -50;

subject to InvBalance[2]:
	-x[2] - s[1] + s[2] = -65;

subject to InvBalance[3]:
	-x[3] - s[2] + s[3] = -100;

subject to InvBalance[4]:
	-x[4] - s[3] + s[4] = -70;


## As it turned out, I made a mistake in setting the ProdCost values
## in the data file: they should've been [5 8 4 7], and not [5 8 7 4]
## as seen above in the expression for NetCost. With the costs set
## wrongly as above, note that we could make infinitely many units of
## the commodity in month 4 at a cost of $4 each, and sell them all
## for $6 at the end of that month to become infinitely rich!

## Fixing that error makes the problem solve correctly.

ampl: reset; model Myinv.mod.txt; data Myinv.dat.txt; solve;
Gurobi 10.0.0: optimal solution; objective 1525
0 simplex iterations
ampl: reset; model Myinv.mod.txt; data Myinv.dat.txt; solve;
Gurobi 10.0.0: optimal solution; objective 1525
0 simplex iterations
ampl: display x, s;
:    x    s     :=
0    .     0
1   115   65
2     0    0
3   170   70
4     0    0
;

ampl: