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GATE 2020 PI – Question 43

Operations Research and Operations Management · Operations Research · 2 marks · Multiple choice

Maximize Z=3x₁+2x₂ subject to x₁+2x₂≤2,2x₁+x₂≤2 and x₁,x₂≥0. Find the shadow price of resource2.

  1. 0
  2. 2/3
  3. 1
  4. 4/3

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Correct answer: (D) 4/3

Explanation

At the optimum both resource constraints bind, giving x₁=x₂=2/3. Dual prices satisfy y₁+2y₂=3 and2y₁+y₂=2 because both products are positive. Solving gives y₁=1/3,y₂=4/3. The resource2 shadow price is4/3, D.

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