For minimization primal all constraints must be ‘≥’ or ‘=’ type, hence Multiplying eq. (i) by -1

-x – 2y ≥ -40 ........................ (p)

3x + y ≥ 30 ........................ (q)

4x + 3y = 60 ....................... (r)

Dual of the above primal is

Maximize

S = -40p + 30q + 60r

Subjected to,

x → -p + 3q + 4r ≤ 20

y → -2p + q + 3r ≤ 10

p, q ≥ 0 ...............................(Since ‘r’ has ‘=’ type equation in primal, hence it is unrestricted)