604-Simple linear programming example using cvxopt.sagews

html("<h2>Simple linear programming example using cvxopt</h2>")
html("Minimize -4*x1-5*x2")
html("Subject to: 2*x1+x2≤ 3")
html("x1+2*x2≤ 3")
html("x1 ≥ 0, x2 ≥ 0")
html("<p></p>")
RealNumber=float
Integer=int
from cvxopt.base import matrix as m
from cvxopt import solvers 
c = m([-4.0, -5.0])
G = m([[2.0, 1., -1.0, 0.0], [1.0, 2.0, 0.0, -1.0]])
h = m([3.0, 3.0, 0.0, 0.0])
sol = solvers.lp(c,G,h)
sol

Simple linear programming example using cvxopt

Minimize -4*x1-5*x2

Subject to: 2*x1+x2≤ 3

x1+2*x2≤ 3

x1 ≥ 0, x2 ≥ 0

pcost dcost gap pres dres k/t 0: -8.1000e+00 -1.8300e+01 4e+00 0e+00 8e-01 1e+00 1: -8.8055e+00 -9.4357e+00 2e-01 1e-16 4e-02 3e-02 2: -8.9981e+00 -9.0049e+00 2e-03 1e-16 5e-04 4e-04 3: -9.0000e+00 -9.0000e+00 2e-05 3e-16 5e-06 4e-06 4: -9.0000e+00 -9.0000e+00 2e-07 1e-16 5e-08 4e-08 {'status': 'optimal', 'x': <2x1 matrix, tc='d'>, 's': <4x1 matrix, tc='d'>, 'z': <4x1 matrix, tc='d'>, 'y': <0x1 matrix, tc='d'>}

html('<h2>Inactive constraint interact example</h2>')
html("Maximize 3*x1+2*x2")
html("Subject to: 2*x1+x2≤ 100")
html("x1+x2≤ 80")
html("x1≤ x0")
html("x1 ≥ 0, x2 ≥ 0")
html("<p></p>")
@interact
def region(x0 = slider(20,60,1)):
    x1,x2,t = var("x1,x2,t")
    line1 = plot(100-2*x1, 0, 50)
    line2 = plot(80-x1, 0, 80)
    line3 = parametric_plot((x0,t), (t, 0, 90))
    reg = region_plot([2*x1+x2<100,x1+x2<80,x1<x0],(x1,0,60),(x2,0,100), plot_points=400, incol='gray')
    show(line1+line2+line3+reg)

html('<h2>Inactive constraint interact example</h2>')
html("Maximize 3*x1+2*x2")
html("Subject to: 2*x1+x2≤ 100")
html("x1+x2≤ 80")
html("x1≤ x0")
html("x1 ≥ 0, x2 ≥ 0")
html("<p></p>")
@interact
def region(x0 = slider(20,60,1)):
    x1,x2,t = var("x1,x2,t")
    line1 = plot(100-2*x1, 0, 50)
    line2 = plot(80-x1, 0, 80)
    line3 = parametric_plot((x0,t), (t, 0, 90))
    reg1 = region_plot([2*x1+x2<100,x1+x2<80],(x1,0,20),(x2,0,100), plot_points=400, incol='gray')
    reg2 = region_plot([2*x1+x2<100,x1+x2<80,x1<x0],(x1,20,60),(x2,0,100), plot_points=400, incol='lightblue')
    show(line1+line2+line3+reg1+reg2)