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GATE 2017 ME (ME2) – Question 58

Operations Research · Network flow models, PERT and CPM · 2 marks · MTA

Factories P and Q supply 7 and 9 units to destinations R and S, each requiring 8 units. Unit transport costs in ₹ are P→R 10, P→S 7, Q→R 3, Q→S 4. Northwest-corner total cost is X and minimum total cost is Y. X−Y is ₹______.

  1. 0
  2. 15
  3. 35
  4. 105

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Correct answer: MTA

Explanation

The final official key awards **marks to all**. For learning, north-west allocation is P→R7, Q→R1, Q→S8, giving X=70+3+32=105rupees. Write P→R=x, P→S=7−x, Q→R=8−x, Q→S=1+x. Cost is77+4x, minimised at x=0, so Y=77 and X−Y=28rupees. None of the displayed choices0,15,35,105 equals28; grading therefore follows marks-to-all.