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$\text{Write the dual of the following LPP}\\ \text{Minimize} \ \ Z = 20x + 10y\\ \text{Subjected to} \\ x + 2y \le 40 .......(i)\\ 3x + y \ge 30........(ii)\\ 4x + 3y = 60.......(iii)\\x, y \ge 0$
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written 7.3 years ago by
teamques10
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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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