Question

This question concerns the dual of this linear program:

max: x + y;
2x + y ≤ 3;
x + 3y ≤ 5;
x ≥ 0;
y ≥ 0;

Assume that the dual uses the two variables a and b.

Which one of the following is a constraint in the dual?

A.) 2a + b ≥ 1

B.) 3a + 2b ≥ 1

C.) a + b ≥ 1

D.) 3a - b ≥ 1

Which one of the following is a constraint in the dual?

A.) a - b ≥ 1

B.) a + 3b ≥ 1

C.) 3a + b ≥ 1

D.) a + 4b ≥ 1

Which one of the following is the objective of the dual?

A.) min: 2a + 4b

B.) min: 3a + 5b

C.) min: 2a + b

D.) min: a + b

Answer 1

The dual of a given maximization problem is a minimization problem and the constraints with greater than equal to symbol. The coefficient matrix of the primal appear as transpose in dual and the R.H.S. of the primal constraints is the coefficient of the dual objective function. the coefficient of the primal objective function makes the R.H.S. of the dual constraints.

So for the given primal problem the dual will be

minimize 3a+5b

subject to

2a+b>=1

a+3b>=1

Hence the answer to your questions are A,B, and B respectively.