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CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Q313 Marksalternative_optima

CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Question 31 (Linear Programming)

For feasible corners (0,10),(5,5),(15,15),(0,20), find p,q>0 such that Z=px+qy is maximal at both (15,15) and (0,20).

✅ Step-by-Step Solution

Final Answer: q=3p.
  1. Equal values at the two specified corners require 15p+15q=20q.
  2. This gives q=3p. The other corner values are 30p and 20p, below 60p.
  3. Thus the equality does give a shared maximum.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Equal values at the two specified corners require 15p+15q=20q.
  • [2 marks] This gives q=3p. The other corner values are 30p and 20p, below 60p.
  • [0.5 marks] Thus the equality does give a shared maximum.

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