Mumbai University > Mechanical Engineering > Sem 7 > Operations Research

Marks: 5 Marks

Year: May 2016

For maximization primal all constraints must be ‘≤’ or ‘=’ type, hence multiplying eq. (ii) by -1.

3x + 2y + 2z ≤ 12 .......................... (p)

-2x -2y – z ≤ -8 ............................... (q)

x + 2y + 3z = 15 .............................(r)

Dual of the above primal is

Minimize

S = 12p – 8q + 15r

Subjected to,

x→ 3p – 2q + r ≥ 3

y→ 2p – 2q + 2r ≥ -8

z→ 2p – q + 3z = 4 ....(Since z is unrestricted in primal hence its constraint equation is of ‘=’ type.)

p, q ≥ 0 ........................(R is unrestricted since equation of this variable in primal is of ‘=’ type.)