# AMPL Session from Lecture 26, Nov 14, 2024

ampl: option solver gurobi;
ampl: reset; model FixedCharge.mod.txt;
ampl: reset; model FixedCharge.mod.txt; data FixedCharge.dat.txt;
ampl: expand NetProfit, MaxRawMatl, ForcingCnstr;
maximize NetProfit:
	2*x[1] + 5*x[2] - 10*y[1] - 20*y[2];

subject to MaxRawMatl:
	3*x[1] + 6*x[2] <= 120;

subject to ForcingCnstr[1]:
	x[1] - 40*y[1] <= 0;

subject to ForcingCnstr[2]:
	x[2] - 20*y[2] <= 0;

ampl: solve; display x,y;
Gurobi 10.0.0: optimal solution; objective 80
1 simplex iterations
1 branching nodes
:   x    y    :=
1    0   0
2   20   1
;

# This happens to be too simple an MIP - Gurobi solves it in the root
# node itself (as indicated by "1 branching nodes").

ampl: expand NetProfit, MaxRawMatl, ForcingCnstr; solve; display x,y;
maximize NetProfit:
	2*x[1] + 5*x[2] - 10*y[1] - 20*y[2];

subject to MaxRawMatl:
	3*x[1] + 6*x[2] <= 120;

subject to ForcingCnstr[1]:
	x[1] - 40*y[1] <= 0;

subject to ForcingCnstr[2]:
	x[2] - 20*y[2] <= 0;

Gurobi 10.0.0: optimal solution; objective 80
0 simplex iterations
1 branching nodes
:   x    y    :=
1    0   0
2   20   1
;

# Relaxing the binary restrictions on y still gives the integer
# optimal solution here, but that's just a lucky incident!

ampl: reset; model FixedCharge.mod.txt; data FixedCharge.dat.txt; solve; display x,y;
Gurobi 10.0.0: optimal solution; objective 80
1 simplex iterations
1 branching nodes
:   x    y    :=
1    0   0
2   20   1
;

ampl: reset; model FixedCharge.mod.txt; data FixedCharge.dat.txt; solve; display x,y;
Gurobi 10.0.0: optimal solution; objective 80
0 simplex iterations
:   x    y    :=
1    0   0
2   20   1
;

# Increasing the per unit profit for Product 1 to $6, which is >$5 for
# Product 2, the optimal solution changes, but it still is too easy an
# MIP to solve.

ampl: reset; model FixedCharge.mod.txt; data FixedCharge.dat.txt; solve; display x,y;
Gurobi 10.0.0: optimal solution; objective 230
1 simplex iterations
:   x    y    :=
1   40   1
2    0   0
;

ampl: reset; model FixedCharge.mod.txt; data FixedCharge.dat.txt; solve; display x,y;
Gurobi 10.0.0: optimal solution; objective 150
1 simplex iterations
:   x    y    :=
1   40   1
2    0   0
;

ampl: