IGNOU AOR 1 2026 - निम्नलिखित LPP की द्वैती लिखिए: का न्यूनतमीकरण कीजिएजबक

Question

निम्नलिखित LPP की द्वैती लिखिए:
$z = 2x_1 + 3x_2 + 4x_3$ का न्यूनतमीकरण कीजिए
जबकि :
$2x_1 + 3x_2 + 5x_3 \ge 2$
$3x_1 + x_2 + 7x_3 = 3$
$x_1 + 4x_2 + 6x_3 \le 5$
$x_1, x_2 \ge 0$ और x₃ अप्रतिबंधित है।

09 Jan 2026

Answer :

Word Count : 285

दिया गया LPP है: Primal Problem (P): Minimize ( z = 2x_1 + 3x_2 + 4x_3 ) subject to: [ \begin{aligned} 2x_1 + 3x_2 + 5x_3 &\ge 2 \quad (1)\ 3x_1 + x_2 + 7x_3 &= 3 \quad (2)\ x_1 + 4x_2 + 6x_3 &\le 5 \quad (3)\ x_1, x_2 \ge 0, \quad x_3 \text{ unrestricted} \end{aligned} ] Step 1: Identify dual variables और नियम * (x_1, x_2 \ge 0 \Rightarrow) उनके लिए dual constraints (\le) और (\le) (as per standard convention for minimization) * (x_3) unrestricted (\Rightarrow) dual constraint (=) (equal) * Constraints types: 1. (\ge) → dual variable (y_1 \le 0) 2. (=) → dual variable (y_2) unrestricted 3.

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