Mathematics · Linear Programming
A company produces products P1, P2, P3 with profits Rs 5, Rs 6, and Rs 4 per unit. Machine hours required are 3, 1, 4 and labour hours are 2, 3, 3 respectively. Total weekly availability is 60 machine hours and 75 labour hours. Which option correctly represents the Primal and Dual formulations to maximize profit?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Minimize Z = 5x1 + 6x2 + 4x3 subject to constraints, and Dual as Maximize Z'
- 2Maximize Z = 5x1 + 6x2 + 4x3 subject to 3x1 + x2 + 4x3 ≤ 60, 2x1 + 3x2 + 3x3 ≤ 75, xi ≥ 0; Dual: Minimize Z' = 60y1 + 75y2 subject to 3y1 + 2y2 ≥ 5, y1 + 3y2 ≥ 6, 4y1 + 3y2 ≥ 4, y1, y2 ≥ 0✓
- 3Maximize Z = 5x1 + 6x2 + 4x3 subject to constraints, and Dual with 3y1 + 2y2 ≤ 5
- 4Maximize Z = 5x1 + 6x2 + 4x3 subject to constraints, and Dual as Maximize Z' = 60y1 + 75y2
Correct answer
Maximize Z = 5x1 + 6x2 + 4x3 subject to 3x1 + x2 + 4x3 ≤ 60, 2x1 + 3x2 + 3x3 ≤ 75, xi ≥ 0; Dual: Minimize Z' = 60y1 + 75y2 subject to 3y1 + 2y2 ≥ 5, y1 + 3y2 ≥ 6, 4y1 + 3y2 ≥ 4, y1, y2 ≥ 0
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