︠32b5fd68-70e1-4ce7-a635-bcea04e239a7ws︠
%typeset_mode True
A = ([-1, 1], [1, 0], [0,1])
b = (1,3,2)
c = (1,1)
P = InteractiveLPProblemStandardForm(A, b, c, ["x1", "x2"])
P.plot()
view(P)
D = P.initial_dictionary()
view(D)
︡d73efbf8-3ad0-4859-a265-b6f4baea2b52︡︡{"file":{"filename":"/projects/d74213da-f29d-4990-b732-706a18b3ab67/.sage/temp/compute0-us/16222/tmp_zdOgtu.svg","show":true,"uuid":"45129e3b-0c60-4e91-924f-9be416f82981"},"once":false}︡{"html":"<div align='center'></div>"}︡{"html":"<div align='center'>$\\displaystyle \\begin{array}{l}\n\\begin{array}{lcrcrcl}\n \\max \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2} \\mspace{-6mu} \\\\\n \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2} \\mspace{-6mu}&amp;\\mspace{-6mu} \\leq \\mspace{-6mu}&amp;\\mspace{-6mu} 1 \\\\\n \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} \\leq \\mspace{-6mu}&amp;\\mspace{-6mu} 3 \\\\\n \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2} \\mspace{-6mu}&amp;\\mspace{-6mu} \\leq \\mspace{-6mu}&amp;\\mspace{-6mu} 2 \\\\\n\\end{array} \\\\\nx_{1}, x_{2} \\geq 0\n\\end{array}$</div>"}︡{"html":"<div align='center'>$\\displaystyle \\renewcommand{\\arraystretch}{1.5}\n\\begin{array}{|rcrcrcr|}\n\\hline\nx_{3} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 1 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\nx_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 3 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} \\\\\nx_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 2 \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\nz \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 0 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\n\\end{array}$</div>"}︡{"done":true}
︠f35a9fab-8430-4d33-9f73-790ff24119cdw︠
D = P.initial_dictionary()
view(D)
print "D jest dopuszczalne: "+ str(D.is_feasible())
print "D jest optmalne: " + str(D.is_optimal())
︡d9ab456f-4462-4613-aa0d-d79ebbe79893︡︡{"html":"<div align='center'>$\\displaystyle \\renewcommand{\\arraystretch}{1.5}\n\\begin{array}{|rcrcrcr|}\n\\hline\nx_{3} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 1 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\nx_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 3 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} \\\\\nx_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 2 \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\nz \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 0 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\n\\end{array}$</div>"}︡{"stdout":"D jest dopuszczalne: True\n"}︡{"stdout":"D jest optmalne: False\n"}︡{"done":true}
︠52ea182f-df2e-4665-a013-fd46e9af5d2f︠
︡acf62dff-b281-40dc-a402-cee3186c56ed︡
︠949ef6dc-3af6-4670-b923-8b99758c6b39w︠
print D.possible_entering()
D.enter("x1")
print D.possible_leaving()
D.leave("x4")
view(D)
︡8e90beb5-8a19-4732-b276-26840d96d56b︡︡{"stdout":"[x1, x2]\n"}︡{"stdout":"[x4]\n"}︡{"html":"<div align='center'>$\\displaystyle \\renewcommand{\\arraystretch}{1.5}\n\\begin{array}{|rcrcrcr|}\n\\hline\nx_{3} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 1 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\color{green}\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\color{red}x_{4} \\mspace{-6mu}&amp;\\color{red}\\mspace{-6mu} = \\mspace{-6mu}&amp;\\color{red}\\mspace{-6mu} 3 \\mspace{-6mu}&amp;\\color{red}\\mspace{-6mu} - \\mspace{-6mu}&amp;\\color{blue}\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\color{red}\\mspace{-6mu}  \\mspace{-6mu}&amp;\\color{red}\\mspace{-6mu} \\\\\nx_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 2 \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\color{green}\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\nz \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 0 \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\color{green}\\mspace{-6mu} x_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\n\\end{array}$</div>"}︡{"done":true}
︠f2ee1558-29ed-4a30-a209-34694405252cw︠
D.update()
view(D)
︡6a6b5d44-180d-4084-9804-3344318dacb4︡︡{"html":"<div align='center'>$\\displaystyle \\renewcommand{\\arraystretch}{1.5}\n\\begin{array}{|rcrcrcr|}\n\\hline\nx_{3} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 4 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\nx_{1} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 3 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{4} \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} \\\\\nx_{5} \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 2 \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu}  \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\nz \\mspace{-6mu}&amp;\\mspace{-6mu} = \\mspace{-6mu}&amp;\\mspace{-6mu} 3 \\mspace{-6mu}&amp;\\mspace{-6mu} - \\mspace{-6mu}&amp;\\mspace{-6mu} x_{4} \\mspace{-6mu}&amp;\\mspace{-6mu} + \\mspace{-6mu}&amp;\\mspace{-6mu} x_{2}\\\\\n\\hline\n\\end{array}$</div>"}︡{"done":true}
︠414cf27f-271e-4bd7-9fdd-eeb6dbe08c80r︠
print D.possible_entering()
︡56b632c4-30e8-431a-aeab-51310d689db2︡
︠9e7ce6e0-efd3-49b6-b38a-732e115db1ec︠











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