︠abd5722b-2853-4008-a67c-56880051d9aes︠
A = ([1, 1], [3, 1], [-1, -1])
b = (1000, 1500, -400)
c = (10, 5)
P = InteractiveLPProblemStandardForm(A, b, c)
view(P)
︡296d36de-1704-4b33-9995-d782d36e9a02︡{"html":"<div align='center'>$\\displaystyle \\begin{array}{l}\n\\begin{array}{lcrcrcl}\n \\max \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} 10 x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} 5 x_{2} \\mspace{-6mu} \\\\\n \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2} \\mspace{-6mu}&amp;\\mspace{-6mu} \\leq \\mspace{-6mu}&amp;\\mspace{-6mu} 1000 \\\\\n \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} 3 x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2} \\mspace{-6mu}&amp;\\mspace{-6mu} \\leq \\mspace{-6mu}&amp;\\mspace{-6mu} 1500 \\\\\n \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2} \\mspace{-6mu}&amp;\\mspace{-6mu} \\leq \\mspace{-6mu}&amp;\\mspace{-6mu} -400 \\\\\n\\end{array} \\\\\nx_{1}, x_{2} \\geq 0\n\\end{array}$</div>"}︡{"done":true}︡
︠5f2ffd44-dc79-4d18-9a7e-3973d54030b1s︠
AP = P.auxiliary_problem()
view(AP)
D = AP.initial_dictionary()
view(D)
D.enter(0)
D.leave(5)
D.update()
view(D)
︡ebf1971f-f520-4e48-bebf-d5ad031c182a︡{"html":"<div align='center'>$\\displaystyle \\begin{array}{l}\n\\begin{array}{lcrcrcrcl}\n \\max \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu} \\\\\n \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2} \\mspace{-6mu}&amp;\\mspace{-6mu} \\leq \\mspace{-6mu}&amp;\\mspace{-6mu} 1000 \\\\\n \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} 3 x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2} \\mspace{-6mu}&amp;\\mspace{-6mu} \\leq \\mspace{-6mu}&amp;\\mspace{-6mu} 1500 \\\\\n \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2} \\mspace{-6mu}&amp;\\mspace{-6mu} \\leq \\mspace{-6mu}&amp;\\mspace{-6mu} -400 \\\\\n\\end{array} \\\\\nx_{0}, x_{1}, x_{2} \\geq 0\n\\end{array}$</div>"}︡{"html":"<div align='center'>$\\displaystyle \\renewcommand{\\arraystretch}{1.5}\n\\begin{array}{|rcrcrcrcr|}\n\\hline\nx_{3} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 1000 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\nx_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 1500 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} 3 x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\nx_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} -400 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\nw \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 0 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} \\\\\n\\hline\n\\end{array}$</div>"}︡{"html":"<div align='center'>$\\displaystyle \\renewcommand{\\arraystretch}{1.5}\n\\begin{array}{|rcrcrcrcr|}\n\\hline\nx_{3} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 1400 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} 2 x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} 2 x_{2}\\\\\nx_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 1900 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} 4 x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} 2 x_{2}\\\\\nx_{0} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 400 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\nw \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} -400 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\n\\end{array}$</div>"}︡{"done":true}︡
︠efb5aadc-2def-4e4e-ae30-a18783079552︠
D.enter(1)
D.leave(0)
D.update()
view(D)
︡38251594-c1ff-412d-bb68-c4978dff6cc9︡{"html":"<div align='center'>$\\displaystyle \\renewcommand{\\arraystretch}{1.5}\n\\begin{array}{|rcrcrcrcr|}\n\\hline\nx_{3} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 600 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} 2 x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} \\\\\nx_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 300 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} 3 x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} 4 x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} 2 x_{2}\\\\\nx_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 400 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\nw \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 0 \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{0} \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} \\\\\n\\hline\n\\end{array}$</div>"}︡{"done":true}︡
︠daaa9003-e967-4915-ab59-480bae0f703fs︠

D.is_optimal()
D.objective_value()
D.basic_solution()
︡db1b2d02-3b18-47c8-b4ed-121884a71c8e︡{"stdout":"True\n"}︡{"stdout":"0\n"}︡{"stdout":"(0, 400, 0)\n"}︡{"done":true}︡
︠3cac036e-885f-4694-9f91-eca332987482s︠

D = P.feasible_dictionary(D)
view(D)
D.is_optimal()
D.is_feasible()
︡e3aef1bb-086a-492a-a56b-396305b53faa︡{"html":"<div align='center'>$\\displaystyle \\renewcommand{\\arraystretch}{1.5}\n\\begin{array}{|rcrcrcr|}\n\\hline\nx_{3} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 600 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} \\\\\nx_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 300 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} 3 x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} 2 x_{2}\\\\\nx_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 400 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\nz \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 4000 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} 10 x_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} 5 x_{2}\\\\\n\\hline\n\\end{array}$</div>"}︡{"stdout":"False\n"}︡{"stdout":"True\n"}︡{"done":true}︡
︠e0187caa-cb22-4761-9e37-c603de96fcf7s︠
D.enter(5)
D.possible_leaving()
︡689affd6-7a60-4e73-978d-6be815f8eb8a︡{"stdout":"[x4]\n"}︡{"done":true}︡
︠bb9b74de-fb63-436d-8c20-f9ad975d7299s︠
D.leave(4)
D.update()
view(D)
︡9787dd9c-ebf5-477d-866f-d40a477e850a︡{"html":"<div align='center'>$\\displaystyle \\renewcommand{\\arraystretch}{1.5}\n\\begin{array}{|rcrcrcr|}\n\\hline\nx_{3} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 500 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{1}{3} x_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{2}{3} x_{2}\\\\\nx_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 100 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{1}{3} x_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{2}{3} x_{2}\\\\\nx_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 500 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{1}{3} x_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{1}{3} x_{2}\\\\\n\\hline\nz \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 5000 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{10}{3} x_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{5}{3} x_{2}\\\\\n\\hline\n\\end{array}$</div>"}︡{"done":true}︡
︠7169e532-3e05-496c-a358-e035e53e0d86s︠
D.enter(2)
D.possible_leaving()
︡eac8f382-de44-42c8-a769-9e06b5ec71cd︡{"stdout":"[x3]\n"}︡{"done":true}︡
︠56785291-a146-472f-90c3-4ee2e0061420s︠
D.leave(3)
D.update()
view(D)
︡1179af1d-66fc-4b84-b7f6-756a9ff623f8︡{"html":"<div align='center'>$\\displaystyle \\renewcommand{\\arraystretch}{1.5}\n\\begin{array}{|rcrcrcr|}\n\\hline\nx_{2} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 750 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{1}{2} x_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{3}{2} x_{3}\\\\\nx_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 600 \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{3}\\\\\nx_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 250 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{1}{2} x_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{1}{2} x_{3}\\\\\n\\hline\nz \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 6250 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{5}{2} x_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} \\frac{5}{2} x_{3}\\\\\n\\hline\n\\end{array}$</div>"}︡{"done":true}︡











Collaborative Calculation and Data Science

colby

sagemath

Product

Resources

Company