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$\text{Write the dual of the following LPP}\\ \text{Minimize} \ \ Z = 20x + 10y\\ \text{Subjected to} \\ x + 2y \le 40 .......(i)\\ 3x + y \ge 30........(ii)\\ 4x + 3y = 60.......(iii)\\x, y \ge 0$
written 7.9 years ago by gravatar for teamques10 teamques10 ★ 68k •   modified 4.0 years ago
operation research
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written 7.9 years ago by gravatar for teamques10 teamques10 ★ 68k

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)
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