MATH2003J, OPTIMIZATION IN ECONOMICS,
BDIC 2023/2024, SPRING
Problem Sheet 6
Question 1:
Solve the following LP problem by the simplex method:
Minimize z = 3x1−2x2
subject to x1 − x2 ≤ 1,
x1 − x2 ≥ −2,
x1, x2 ≥ 0.
Question 2:
Solve the following LP problem by the simplex method:
Maximize z = 8x1 + 2x2+2x3
subject to 2x1 + x2 + 4x3 ≤ 60,
−x2 − x3 ≤ −40,
x1, x2, x3 ≥ 0.
Question 3:
Solve the following LP problem by the simplex method:
Maximize z = 4x1+5x2
subject to x1 + 2x2 ≤ 20,
x1 + x2 ≤ 18,
2x1 + x2 ≥ 12,
x1, x2 ≥ 0.
Question 4:
Solve the following LP problem by the simplex method:
Minimize z = 2x1 − 3x2+x3
subject to 2x1 − x2 + 3x3 ≤ 7,
−4x2 + 2x3 ≥ 12,
8x1 + 3x2 − 4x3 ≤ 10,
x1, x2, x3 ≥ 0.
Question 5:
Solve the following LP problem by the simplex method:
Minimize z = x1 + x2 + 2x3
subject to x1 + 2x2 − x3 ≥ 8,
x1 + x2 − 2x3 ≤ 10,
x1, x2, x3 ≥ 0.
Question 6:
Solve the following LP problem by the simplex method:
Maximize z = 5x1 + 4x2
subject to 2x1 + x2 ≤ 20,
x1 + x2 ≤ 18,
x1 + 2x2 = 12,
x1, x2 ≥ 0.
Question 7:
Solve the following LP problem by the simplex method:
Maximize z = 2x1 − 3x2
subject to x1 + x2 ≤ 10,
x1 − x2 ≤ 12,
2x1 − x2 ≥ 6,
x1 ≥ 0.
Question 8:
Solve the following LP problem by the simplex method:
Minimize z = 2x1 + 3x2
subject to − x1 + x2 ≤ 10,
−x1 − x2 ≤ 12,
−2x1 − x2 ≥ 6,
x1 ≥ 0, x2 ≤ 0.
Question 9:
Solve the following LP problem by the simplex method:
Minimize z = x1 + x2
subject to 2x1 + x2 ≥ 16,
x1 + 2x2 ≥ 20,
x1, x2 ≥ 0.