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CA Foundation · Quantitative Aptitude · Linear Inequalities

A manufacturing firm produces two products P and Q. Product P yields a profit of ₹ 8 per unit and Product Q yields ₹ 12 per unit. The firm has production capacity constraints: at most 600 units of P and at most 400 units of Q can be produced weekly. Additionally, the total production cannot exceed 800 units per week. If x units of P and y units of Q are produced, which inequality does NOT form part of the constraint set?

The firm's constraints are x ≤ 600, y ≤ 400, and x + y ≤ 800. The inequality x + y ≥ 800 does not form part of the constraints because it requires production to exceed the maximum capacity of 800 units, contradicting the given capacity limit.

  1. Ax ≤ 600
  2. By ≤ 400
  3. Cx + y ≤ 800
  4. Dx + y ≥ 800Correct

Explanation

The constraints are: x ≤ 600 (max P units), y ≤ 400 (max Q units), and x + y ≤ 800 (total capacity). The inequality x + y ≥ 800 means total production must be at least 800 units, which contradicts the capacity constraint that total cannot exceed 800 units. Therefore, x + y ≥ 800 is NOT part of the valid constraint set.

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