NCERT Class 12 · Ch 12 Exercise 12.1 · Q10
NCERT Class 12 Maths · Chapter 12 Linear Programming · Exercise 12.1 Question 10
Maximize Z=x+y subject to x−y≤−1,−x+y≤0,x,y≥0. Solve graphically.
💡 Concept Hints
- Convert the inequalities to boundary lines and identify the common feasible region.
- Evaluate the objective at all feasible vertices, then check directions of escape if the region is unbounded.
✅ Step-by-Step Solution
Final Answer: No feasible solution; neither a maximum nor a minimum exists.
- Draw the boundary lines y=x+1 and y=x in the first quadrant.
- The first inequality requires y≥x+1, while the second requires y≤x.
- Adding x−y≤−1 and −x+y≤0 would give 0≤−1, a contradiction. The half-planes have no intersection.
- Therefore the LPP is infeasible; an objective optimum cannot be assigned.
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