[SOLVED] MATH2003J OPTIMIZATION IN ECONOMICS BDIC 2023/2024 SPRING Problem Sheet 7Haskell

MATH2003J, OPTIMIZATION IN ECONOMICS,

BDIC 2023/2024, SPRING

Problem Sheet 7

Question 1:

Formulate the dual problem of the LP problem:

Maximize z = −3×1 + 2×2

subject to x1 − x2 ≤ 3,

−x1 + x2 ≤ 6,

x1, x2 ≥ 0.

Question 2:

Formulate the dual problem of the LP problem:

Maximize z = 16×1 + 25×2

subject to x1 + 2×2 ≤ 20,

x1 − x2 ≤ 18,

−2×1 + x2 ≤ 12,

x1, x2 ≥ 0.

Question 3:

Formulate the dual problem of the LP problem:

Maximize z = 8×1 + 2×2−2×3

subject to 2×1 − x2 + 4×3 ≤ 60,

x2 − x3 ≤ 40,

x1, x2, x3 ≥ 0.

Question 4:

Formulate the dual problem of the LP problem:

Maximize z = 8×1 − 3×2+x3

subject to 2×1 − x2 + 3×3 ≤ 27,

3×2 − 4×3 ≤ 15,

6×1 + 3×2 − 4×3 ≤ 22,

x1, x2, x3 ≥ 0.

Question 5:

Formulate the dual problem of the LP problem:

Maximize z = 3×1 − x2 + 8×3

subject to x1 + 2×2 − x3 ≤ 28,

x1 − 2×2 ≤ 16,

x1, x2, x3 ≥ 0.

Question 6:

Formulate the dual problem of the LP problem:

Maximize z = 2×1 − 3×2 + x3

subject to x1 + 3×2 + x3 ≤ 18,

6×1 − x2 ≤ 16,

8×1 − 2×2 + 2×3 ≤ 32,

x1, x2, x3 ≥ 0.

Question 7:

Formulate the dual problem of the LP problem:

Maximize z = 2×1 + 3×2 − x3 + 3×4

subject to − x1 + x2 + 2×3 ≤ 21,

2×1 − x2 + 4×4 ≤ 25,

3×1 + 8×2 − x4 ≤ 36,

x1, x2, x3, x4 ≥ 0.