Question

Solve the following LPP using two-phase method.
Min Z = -3x - 2y - 2z
s.t. 5x + 7y + 4z > 7
- 4x + 7y + 5z > -2
3x + 4y - 6z > 29 / 7
x, y, z > 0.

14 Feb 2018
Answer :
Word Count : 552
To solve the given Linear Programming Problem (LPP) using the two-phase method, we will proceed through the following steps: ### Problem: Minimize \( Z = -3x - 2y - 2z \) Subject to: 1. \( 5x + 7y + 4z \geq 7 \) 2. \( -4x + 7y + 5z \geq -2 \) 3. \( 3x + 4y - 6z \geq \frac{29}{7} \) 4. \( x, y, z \geq 0 \) ### Step 1: Convert inequalities to standard form We need to convert all inequalities to equality by introducing slack, surplus, or artificial variables as appropriate. The general steps for handling inequalities: - For \( \geq \) inequalities, we introduce a surplus variable \( s \) and an artificial variable \( a \). - For \( \leq \) inequalities, we introduce a
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