[SOLVED] MATH2003J OPTIMIZATION IN ECONOMICS BDIC 2023/2024 SPRING Problem Sheet 6 Matlab

MATH2003J, OPTIMIZATION IN ECONOMICS,

BDIC 2023/2024, SPRING

Problem Sheet 6

Question 1:

Solve the following LP problem by the simplex method:

Minimize z = 3×1−2×2

subject to x1 − x2 ≤ 1,

x1 − x2 ≥ −2,

x1, x2 ≥ 0.

Question 2:

Solve the following LP problem by the simplex method:

Maximize z = 8×1 + 2×2+2×3

subject to 2×1 + x2 + 4×3 ≤ 60,

−x2 − x3 ≤ −40,

x1, x2, x3 ≥ 0.

Question 3:

Solve the following LP problem by the simplex method:

Maximize z = 4×1+5×2

subject to x1 + 2×2 ≤ 20,

x1 + x2 ≤ 18,

2×1 + x2 ≥ 12,

x1, x2 ≥ 0.

Question 4:

Solve the following LP problem by the simplex method:

Minimize z = 2×1 − 3×2+x3

subject to 2×1 − x2 + 3×3 ≤ 7,

−4×2 + 2×3 ≥ 12,

8×1 + 3×2 − 4×3 ≤ 10,

x1, x2, x3 ≥ 0.

Question 5:

Solve the following LP problem by the simplex method:

Minimize z = x1 + x2 + 2×3

subject to x1 + 2×2 − x3 ≥ 8,

x1 + x2 − 2×3 ≤ 10,

x1, x2, x3 ≥ 0.

Question 6:

Solve the following LP problem by the simplex method:

Maximize z = 5×1 + 4×2

subject to 2×1 + x2 ≤ 20,

x1 + x2 ≤ 18,

x1 + 2×2 = 12,

x1, x2 ≥ 0.

Question 7:

Solve the following LP problem by the simplex method:

Maximize z = 2×1 − 3×2

subject to x1 + x2 ≤ 10,

x1 − x2 ≤ 12,

2×1 − x2 ≥ 6,

x1 ≥ 0.

Question 8:

Solve the following LP problem by the simplex method:

Minimize z = 2×1 + 3×2

subject to − x1 + x2 ≤ 10,

−x1 − x2 ≤ 12,

−2×1 − x2 ≥ 6,

x1 ≥ 0, x2 ≤ 0.

Question 9:

Solve the following LP problem by the simplex method:

Minimize z = x1 + x2

subject to 2×1 + x2 ≥ 16,

x1 + 2×2 ≥ 20,

x1, x2 ≥ 0.