Question

Duality Theory: Consider the following LP:

max 2x1+2x2+4x3

x1−2x2+2x3≤−1

3x1−2x2+4x3≤−3

x1,x2,x3≤0

Formulate a dual of this linear program. Select all the correct objective function and constraints

1. min −y1−3y2

2. min −y1−3y2

3. y1+3y2≤2

4. −2y1−2y2≤2

5. 2y1+4y2≤4

6. y1,y2≤0

Answer 1

The given problem in matrix form we can write as

subject to constraints

where

, , and

Since the primal has objective maximize, dual has objective minimize and dual is given by

subject to the constaints

where

So we can write the dual of given linear programming problem as

subject to constaints

So the correct objective function of dual is

Correct constraints of dual are