# Define the data
m = 3
n = 4
c = [1.5; 2.5; 3.0; 4.5]
A = [2 4 3 7;
     3 2 3 4;
     2 3 2 5]
b = [100000; 50000; 60000]

# Import necessary packages and define model
using JuMP
using Gurobi  # We need Gurobi for Sensitivity Analysis later
model = Model(solver=GurobiSolver())

# Define the variables
@variable(model, x[i=1:n] >= 0)

# Add the objective
@objective(model, Max, sum{c[i] * x[i], i=1:n})

# Add the constraints row-by-row, naming them according to each resource
# The names will allow us to refer to the constraints during sensitivity analysis
@constraint(model, assembly, dot(vec(A[1,:]), x) <= b[1])
@constraint(model, polish,   dot(vec(A[2,:]), x) <= b[2])
@constraint(model, pack,     dot(vec(A[3,:]), x) <= b[3])

# Solve the model and show the optimal solution and objective value
solve(model)
@show getvalue(x)
@show getobjectivevalue(model);

x_final = getvalue(x)

con_final = A * x_final

red_costs = getdual(x)

getdual(assembly)

getdual(polish)

getdual(pack)

shadow_prices = getdual([assembly; polish; pack])

obj_coeff = c

con_rhs = b

# Import Gurobi so we can access the API
import Gurobi

# Get a reference to the internal Gurobi model so we can use the API
g = getrawsolver(model)

# RHS value lower and upper bounds
rhs_lb = Gurobi.get_dblattrarray(g, "SARHSLow", 1, m)
rhs_ub = Gurobi.get_dblattrarray(g, "SARHSUp", 1, m)
@show rhs_lb
@show rhs_ub

# Objective coefficient lower and upper bounds
obj_lb = Gurobi.get_dblattrarray(g, "SAObjLow", 1, n)
obj_ub = Gurobi.get_dblattrarray(g, "SAObjUp", 1, n)
@show obj_lb
@show obj_ub;

x_order = map(linearindex, x)

con_order = map(linearindex, [assembly, polish, pack])

rhs_lb_sorted = rhs_lb[con_order];
rhs_ub_sorted = rhs_ub[con_order];
obj_lb_sorted = obj_lb[x_order];
obj_ub_sorted = obj_ub[x_order];

@show rhs_dec = con_rhs - rhs_lb_sorted;
@show rhs_inc = rhs_ub_sorted - con_rhs;

@show obj_dec = obj_coeff - obj_lb_sorted;
@show obj_inc = obj_ub_sorted - obj_coeff;

var_sensitivity = [x_final red_costs obj_coeff obj_inc obj_dec]

con_sensitivity = [con_final shadow_prices con_rhs rhs_inc rhs_dec]