Pesquisa operacional graficos

Lista 01 – Método Gráfico – Gabarito

1) Min Z = 4X1 + 5X2 s.a. X1 + X2 ≤ 4 1 X2 ≥ 3 2 X1, X2 ≥ 0

Z* = 15 X1* = 0 X2* = 3

2) Max Z = 4X1 + 5X2 s.a. X1 + X2 ≤ 4 1 X2 ≥ 3 2 X1, X2 ≥ 0

Z* = 20 X1* = 0 X2* = 4

3) Max Z = 4X1 + 5X2 s.a. X1 + X2 ≥ 4 1 X2 ≥ 3 2 3X1 + X2 ≤ 10 3 X1, X2 ≥ 0

Z* = 50 X1* = 0 X2* = 10

4) Max Z = 10X1 + 8X2 s.a. 3X1 + 3X2 ≤ 30 1 6X1 + 3X2 ≤ 48 2 X1, X2 ≥ 0

Z* = 92 X1* = 6 X2* = 4

5) Max L = 4X1 + X2 s.a. 2X1 + 3X2 ≤ 12 1 2X1 + X2 ≤ 8 2 X1, X2 ≥ 0

Z* = 16 X1* = 4 X2* = 0

6) Max Z = X1 + 2X2 s.a. X 1 + X2 ≥ 3 1 X1 ≥ 2 2 X2 ≤ 2 3 X1, X2 ≥ 0

Solução Ilimitada

7) Max Z = 2X1 + X2 s.a. X1 + X2 ≤ 10 1 X1 ≥ 2 2 X2 ≥ 3 3 X1, X2 ≥ 0

Z* = 17 X1* = 7 X2* = 3

8) Max Z = 2X1 + X2 s.a. X1 + X2 ≤ 10 1 3X1 + X2 ≥ 18 2 X2 ≥ 3 3 X1, X2 ≥ 0

Z* = 17 X1* = 7 X2* = 3

9) Max Z = 2X1 + X2 s.a. 3X1 + X2 ≤ 18 1 X1 + X2 ≥ 10 2 X1 ≥ 2 3 X1, X2 ≥ 0

Z* = 16 X1* = 2 X2* = 12

10) Max Z = - X1 + 2X2 s.a. -X1 + X2 ≥ 1 1 X1 – 2X2 ≥