Q6Advanced Engineering Mathematics

Question

Write the dual of:

Max z = x_{1} + 3 x_{2} Subject to: 3 x_{1} + 2 x_{2} \leq 6 3 x_{1} + x_{2} = 4 x_{1}, x_{2} \geq 0

Answer 1

Given Primal Problem: Max $z = x_{1} + 3 x_{2}$ Subject to: $3 x_{1} + 2 x_{2} \leq 6$ (Constraint 1, $\leq$ type $⟹$ dual variable $w_{1} \geq 0$ ) $3 x_{1} + x_{2} = 4$ (Constraint 2, equality type $⟹$ dual variable $w_{2}$ is unrestricted in sign) $x_{1}, x_{2} \geq 0$

Min Z_{d} = 6 w_{1} + 4 w_{2} Subject to: 3 w_{1} + 3 w_{2} \geq 1 2 w_{1} + w_{2} \geq 3 w_{1} \geq 0, w_{2} is unrestricted in sign.

Q6Advanced Engineering Mathematics

Question

Answer