IGNOU AOR 1 2026 - Use branch and bound method to solve the following LPP:Minimize: Z

Question

Use branch and bound method to solve the following LPP:

Minimize: Z = 4x₁ + 3x₂

Subject to the constraints:

$$5x_1 + 3x_2 \geq 30$
$$x_1 \leq 4$
$$x_2 \leq 6$
$x_1, x_2 \geq 0$ and are integers.

09 Jan 2026

Answer :

Word Count : 591

Minimize: ( Z = 4x_1 + 3x_2 ) Subject to: ( 5x_1 + 3x_2 \geq 30 ), ( x_1 \leq 4 ), ( x_2 \leq 6 ), ( x_1, x_2 \geq 0 ) and integers. Step 1: Solve the relaxed LPP (ignore integer constraints). Constraints: 1. ( 5x_1 + 3x_2 \geq 30 ) → ( x_2 \geq \frac{30 - 5x_1}{3} ) 2. ( x_1 \leq 4 ) 3. ( x_2 \leq 6 ) 4. ( x_1, x_2 \geq 0 ) Step 2: Find feasible region vertices. * Intersection of ( 5x_1 + 3x_2 = 30 ) and ( x_1 = 4 ): ( 5(4) + 3x_2 = 30 ) → ( 20 + 3x_2 = 30 ) → ( 3x_2 = 10 ) → ( x_2 = \frac{10}{3} \approx 3.333 ) → Z = ( 4*4 + 3*(10/3) = 16 + 10 = 26 ) * Intersection of ( 5x_1 + 3x_2 = 30 ) and ( x_2 = 6 ): ( 5x_1 + 3*6 = 30 ) → ( 5x_1 + 18 = 30 ) →

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