Write the dual of the following LP problem:Min. Sub

Question

Write the dual of the following LP problem:

Min. $Z=3x_1-2x_2+4x_3$

Subject to

$3x_1+5x_2+4x_3\geq 7$

$6x_1+x_2+3x_3=4$

$7x_1-2x_2-x_3\leq 10$

$x_1,x_2,x_3\leq0$

10 Mar 2024

Answer :

Word Count : 339

To write the dual of the given linear programming (LP) problem, we need to follow these steps:

1. Replace each inequality constraint with a dual variable and write the corresponding dual constraint.
2. Replace each equality constraint with a dual variable and write the corresponding dual constraint.
3. If the primal problem is a minimization problem, then the dual problem will be a maximization problem, _____ _____ _______ _________ ________ ______ _________.
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Activity	Estimated duration (in days)
Activity	Optimistic	Most likely	Pessimistic
A (1, 2)	28	32	36
B (1,3)	22	28	32
C (2, 6)	26	36	46
D (3, 4)	14	16	18
E (3, 5)	32	32	32
F (3, 6)	40	52	74
G (4, 5)	12	16	24
H (5, 6)	16	20	26

Factory	Ware house	$W_1$	$W_2$	$W_2$	Availability
$F_1$		16	20	12	200
$F_2$		14	8	18	160
$F_3$		26	24	16	90
Demand		180	120	150