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CA Foundation · Quantitative Aptitude · Linear Inequalities

A manufacturing unit produces two products, A and B. The profit per unit of A is ₹50 and per unit of B is ₹40. If x units of A and y units of B are produced, and the constraint is that total production cannot exceed 200 units, which inequality correctly represents this constraint?

The correct inequality is x + y ≤ 200. Since total production cannot exceed 200 units, we add the number of units of A and B and set it less than or equal to 200. Using profit values or ≥ signs would misrepresent the constraint.

  1. Ax + y ≤ 200Correct
  2. B50x + 40y ≤ 200
  3. Cx + y ≥ 200
  4. D50x + 40y ≥ 200

Explanation

The constraint 'total production cannot exceed 200 units' means the sum of units of both products must be at most 200. This translates to x + y ≤ 200. Option (2) incorrectly uses profit values instead of unit counts. Options (3) and (4) use ≥ which contradicts 'cannot exceed'.

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