using Polyhedra
h = HalfSpace([-1, 0], 1) ∩ HalfSpace([1, 0], 1) ∩ HalfSpace([-4, -1], 1) ∩ HalfSpace([2, -1], 1) ∩
    HalfSpace([-1/4, -1], 0) ∩ HalfSpace([1/2, -1], 0)

using CDDLib
p = polyhedron(h, CDDLib.Library())

vrep(p)

p

using Plots
plot(p ∩ HalfSpace([0, 1], 4))
scatter!([x[1] for x in points(p)], [x[2] for x in points(p)])

using JuMP
model = Model(Polyhedra.linear_objective_solver(p))
@variable(model, x)
@variable(model, y)
@constraint(model, [x, y] in p)
@objective(model, Min, x + y)
optimize!(model)

termination_status(model)

value(x), value(y)

plot!([-0.2, -1.2], [0.0, 1.0], linewidth=2) # Objective function
scatter!([value(x)], [value(y)], markershape=:star5, markersize=8) # Optimal solution

@objective(model, Max, x + y)
optimize!(model)

termination_status(model)

value(x), value(y)

using JuMP
import GLPK
model = Model(GLPK.Optimizer)
@variable(model, x <= -2)
@variable(model, y)
@variable(model, 0 <= u <= 3)
@constraint(model, [2x + u, y] in p)
@objective(model, Min, u + y)
optimize!(model)

termination_status(model)

value(x), value(y), value(u)

using Polyhedra
h = HalfSpace([-1, 0, 0], 1) ∩ HalfSpace([1, 0, 0], 1) ∩
    HalfSpace([0, -1, 0], 1) ∩ HalfSpace([0, 1, 0], 1) ∩
    HalfSpace([-4, -2, -1], 1) ∩ HalfSpace([2, -1, -1], 1) ∩
    HalfSpace([-1/4, 1/2, -1], 0) ∩ HalfSpace([1/2, 1, -1], 0)

using CDDLib
p = polyhedron(h, CDDLib.Library())

vrep(p)

m = Polyhedra.Mesh(p)

using MeshCat
vis = Visualizer()
setobject!(vis, m)
IJuliaCell(vis)

using Makie
Makie.mesh(m, color=:blue)

using Makie
Makie.wireframe(m)