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CA Foundation · Quantitative Aptitude · Linear Inequalities

A shop sells two types of bags, x units of type A and y units of type B. Each type A bag needs 2 hours of stitching and each type B bag needs 3 hours. At most 60 hours of stitching are available, and the shop must make at least 5 bags of type A. Which set of inequalities represents this situation?

The correct constraints are 2x + 3y ≤ 60, x ≥ 5 and y ≥ 0. Total stitching hours are 2x + 3y, limited to at most 60 hours; at least 5 type A bags means x ≥ 5, and type B output cannot be negative.

  1. A2x + 3y ≤ 60, x ≥ 5, y ≥ 0Correct
  2. B2x + 3y ≥ 60, x ≥ 5, y ≥ 0
  3. C3x + 2y ≤ 60, x ≥ 5, y ≥ 0
  4. D2x + 3y ≤ 60, x ≤ 5, y ≥ 0

Explanation

Stitching time used is 2x + 3y, and this cannot exceed 60, so 2x + 3y ≤ 60. At least 5 of type A gives x ≥ 5. Number of bags cannot be negative, so y ≥ 0. Option C swaps the hours per bag, a coefficient mix-up.

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