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📐 Mathematics  ·  Linear Programming  ·  JEE

Continuing the furniture problem (Z = 30x + 60y, corners (0,0), (20,0), (12,16), (0,20)), what is the maximum profit?

Answer: 1320.

  • A 1320
  • B 600
  • C 1200
  • D 960

Correct answer: A. 1320

Explanation: Corner-point method: Z(0,0)=0; Z(20,0)=600; Z(12,16)=30(12)+60(16)=360+960=1320; Z(0,20)=0+1200=1200. Largest value is 1320 at (12,16). Answer: maximum profit = Rs 1320.

Feasible Region and Corner PointsxyOABCfeasible regionZ = ax+by is evaluated ONLY at corners O, A, B, C - the optimum is always at one of these

The feasible region (shaded) is bounded by the constraint lines; the fundamental theorem of LPP guarantees the optimal value of the objective function occurs at one of the corner points (O, A, B, C), so only these need to be checked, not the entire region.

Concept context

Optimizing a linear objective function subject to linear constraints using the graphical corner point method.

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