代写MATH2003J, OPTIMIZATION IN ECONOMICS, BDIC 2023/2024, SPRING Problem Sheet 7调试Haskell程序

MATH2003J, OPTIMIZATION IN ECONOMICS,

BDIC 2023/2024, SPRING

Problem Sheet 7

Question 1:

Formulate the dual problem of the LP problem:

Maximize z = −3x1 + 2x2

subject to x1 − x2 ≤ 3,

−x1 + x2 ≤ 6,

x1, x2 ≥ 0.

Question 2:

Formulate the dual problem of the LP problem:

Maximize z = 16x1 + 25x2

subject to x1 + 2x2 ≤ 20,

x1 − x2 ≤ 18,

−2x1 + x2 ≤ 12,

x1, x2 ≥ 0.

Question 3:

Formulate the dual problem of the LP problem:

Maximize z = 8x1 + 2x2−2x3

subject to 2x1 − x2 + 4x3 ≤ 60,

x2 − x3 ≤ 40,

x1, x2, x3 ≥ 0.

Question 4:

Formulate the dual problem of the LP problem:

Maximize z = 8x1 − 3x2+x3

subject to 2x1 − x2 + 3x3 ≤ 27,

3x2 − 4x3 ≤ 15,

6x1 + 3x2 − 4x3 ≤ 22,

x1, x2, x3 ≥ 0.

Question 5:

Formulate the dual problem of the LP problem:

Maximize z = 3x1 − x2 + 8x3

subject to x1 + 2x2 − x3 ≤ 28,

x1 − 2x2 ≤ 16,

x1, x2, x3 ≥ 0.

Question 6:

Formulate the dual problem of the LP problem:

Maximize z = 2x1 − 3x2 + x3

subject to x1 + 3x2 + x3 ≤ 18,

6x1 − x2 ≤ 16,

8x1 − 2x2 + 2x3 ≤ 32,

x1, x2, x3 ≥ 0.

Question 7:

Formulate the dual problem of the LP problem:

Maximize z = 2x1 + 3x2 − x3 + 3x4

subject to − x1 + x2 + 2x3 ≤ 21,

2x1 − x2 + 4x4 ≤ 25,

3x1 + 8x2 − x4 ≤ 36,

x1, x2, x3, x4 ≥ 0.