Teaching UGC NET Mock Test Series 2025 (Paper 1 & 2) Mathematical Science LPP, Simplex Methods, Duality
Comprehension Passage
A company manufactures two products, A and B. Each unit of Product A requires 3 hours in Workshop X and 1 hour in Workshop Y. Each unit of Product B requires 2 hours in Workshop X and 2 hours in Workshop Y. The profit per unit on Product A is $30, and the profit per unit on Product B is $40. If Workshop X is available for 18 hours per day and Workshop Y for 8 hours per day
Identify the correct duality of the given question:
1
Minimize Z = 18u + 8v
Subject to:
3u + v ≥ 30
2u + 2v ≥ 40, u ≥ 0, v ≥ 0
2
Minimize Z = 30u + 40v
Subject to:
3u + v ≥ 8
2u + 2v ≥ 18, u ≥ 0, v ≥ 0
3
Minimize Z = 18u + 8v
Subject to:
3u + 2v ≥ 30
u + 2v ≥ 40, u ≥ 0, v ≥ 0
4
Minimize Z = 40u + 30v
Subject to:
3u + v ≥ 18
2u + 2v ≥ 8, u ≥ 0, v ≥ 0