Class 12 Linear Programming · Long Answer3 Marksgraphical_optimization
Class 12 Maths · Linear Programming · Long Answer #59
Z=ax+by has the same optimal value at distinct feasible points (2,3),(5,7). Derive a relation between a,b.
✅ Step-by-Step Solution
Final Answer: 3a+4b=0.
- Equal optimal values imply Z(2,3)=Z(5,7).
- Thus 2a+3b=5a+7b.
- Rearrange: 3a+4b=0. This necessary relation alone does not establish optimality on an unspecified region.
- The required relation is 3a+4b=0.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Equal optimal values imply Z(2,3)=Z(5,7).
- [1 mark] Thus 2a+3b=5a+7b.
- [1 mark] Rearrange: 3a+4b=0. This necessary relation alone does not establish optimality on an unspecified region.
- [0.5 marks] The required relation is 3a+4b=0.
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