solutions MA

Assignment Details

• Course: Lan V. Truong

• Submission Platform: Faser

• Deadline: 22/03/2024 at 12 pm

• Total Marks: 100

Problem 1: Converting LP to Dual Form [30 marks]

• Objective Function:

  • Minimize: 3x1 − x2 + x3

• Subject to Constraints:

  1. x1 − 2x2 − x3 ≤ 4

  2. 2x1 − x2 + x3 = 8

  3. x1 − x2 ≤ 6

• Variable Constraints:

  • x1 ≥ 0;

  • x2, x3 are free.

Problem 2: Optimality Check using Complementary Slackness [40 marks]

• Candidate Solution:(x1, x2, x3, x4) = (0, 14, 0, 5)

• Objective Function:

  • Maximize: 4x1 + x2 + 5x3 + 3x4

• Subject to Constraints:

  1. x1 − x2 − x3 + 3x4 ≤ 1

  2. 5x1 + x2 + 3x3 + 8x4 ≤ 5

  3. −x1 + 2x2 + 3x3 − 5x4 ≤ 3

• Variable Constraints:

  • x1, x2, x3, x4 ≥ 0

Problem 3: Solving LP with Dual Simplex Method [30 marks]

• Objective Function:

  • Minimize: 3x1 + 2x2 + 10

• Subject to Constraints:

  1. 3x1 + x2 ≥ 3

  2. 4x1 + 3x2 ≥ 6

• Variable Constraints:

  • x1 ≥ 1;

  • x2 is free.