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📐 Mathematics  ·  Linear Programming  ·  JEE

A diet problem requires at least 8 units of vitamin A and at least 11 units of vitamin B daily. Food 1 (x units) gives 2 units of A and 1 unit of B per item; Food 2 (y units) gives 1 unit of A and 2 units of B per item. Which constraints model the minimum requirements?

Answer: 2x + y >= 8 and x + 2y >= 11.

  • A 2x + y >= 8 and x + 2y >= 11
  • B 2x + y <= 8 and x + 2y <= 11
  • C x + 2y >= 8 and 2x + y >= 11
  • D 2x + y >= 11 and x + 2y >= 8

Correct answer: A. 2x + y >= 8 and x + 2y >= 11

Explanation: Vitamin A requirement: 2 units from Food 1 plus 1 unit from Food 2 per item, total at least 8: 2x + y >= 8. Vitamin B: 1 unit from Food 1 plus 2 units from Food 2, total at least 11: x + 2y >= 11.

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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