Atividade simplex

Atividades

A) P = 3x+5y P-3x-5y=0 x <= 4 x+a = 4
2y <= 12 2y+b = 12
3x+2y <= 18 3x+2y+c = 18 x >= 0 y >= 0

Reescrevendo as equações
P = 0
A=2
Y+1/2b = 6
X+1/3c = 2

P | x | y | a | b | c | valor | | 1 | -3 | -5 | 0 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | 0 | 4 | | 0 | 0 | 2 | 0 | 1 | 0 | 12 | | 0 | 3 | 2 | 0 | 0 | 1 | 18 | | Resultado | P | x | y | a | b | c | valor | | 1 | -3 | 0 | 0 | 0 | 0 | 0 | L1+5L3 | 0 | 1 | 0 | 1 | 0 | 0 | 4 | L4-2L3 | 0 | 0 | 1 | 0 | 1/2 | 0 | 6 | | 0 | 3 | 0 | 0 | 0 | 1 | 6 | | Escolhendo novo pivô | P | x | y | a | b | c | valor | | 1 | -3 | 0 | 0 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | 0 | 4 | | 0 | 0 | 1 | 0 | 1/2 | 0 | 6 | | 0 | 3 | 0 | 0 | 0 | 1 | 6 | | Resultado | P | x | y | a | b | c | valor | | 1 | 0 | 0 | 0 | 0 | 0 | 0 | L1+3L4 | 0 | 0 | 0 | 1 | 0 | 0 | 2 | L2-L4 | 0 | 0 | 1 | 0 | 1/2 | 0 | 6 | | 0 | 1 | 0 | 0 | 0 | 1/3 | 2 | |

B) P = 2x+y P-2x-y=0
Y<=10 y+a=10
2x+5y<=60 2x+5y+b=60
X+y<=18 x+y+c=18
3x+y<=44 3x+y+d=44

P | x | y | a | b | c | d | valor | | 1 | -2 | -1 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 10 | | 0 | 2 | 5 | 0 | 1 | 0 | 0 | 60 | | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 18 | | 0 | 3 | 1 | 0 | 0 | 0 | 1 | 44 | | Resultado | P | x | y | a | b | c | d | valor | | 1 | 0 | 1/3 | 0 | 0 | 0 | 0 | 0 | L1+2L5 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 10 | | 0 | 0 | 4 1/3 | 0 | 1 | 0 | 0 | 30 2/3 | L3-2L5 | 0 | 0 | 2/3 | 0 | 0 | 0 | 0 | 3 1/3 | L4-L5 | 0 | 1 | 1/3 | 0 | 0 | 0 | 1/3 | 14 2/3 | |

Reescrevendo as equações
P + 1/3y = 0
Y+a = 10 a = 5
13/3y+b = 92/3
2/3y = 10/3 y = 5
X+1/3y+1/3d = 44/3

C) P = -2x-2y P+2x-2y = 0
3x-4Y <= 18 3x-4y+a = 18
8x-3y <= -24 8x-3y+b = -24
6X+8y <= 24 6x+8y+c = 24
3X+5y <= 21 3x+5y+d = 21

P | x | y | a | b | c | d | valor | | 1 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | | 0 | 3 | -4 | 1 | 0