CA Foundation · Quantitative Aptitude · Linear Inequalities
A company produces toys in batches. Let x be the number of standard batches and y be the number of deluxe batches. Standard batches require 10 labour-hours each, and deluxe batches require 15 labour-hours each. The company has 1200 labour-hours available monthly. Also, due to machine constraints, the company must produce at least 20 standard batches monthly. Which inequality correctly represents the labour-hour constraint?
Labour-hours used is 10x + 15y. Since the company has only 1200 labour-hours available, total usage cannot exceed this amount. The constraint is 10x + 15y ≤ 1200, representing that actual labour-hours used must not exceed the available capacity.
- A10x + 15y = 1200
- B10x + 15y ≤ 1200Correct
- C10x + 15y ≥ 1200
- Dx + y ≤ 1200
Explanation
Total labour-hours used = 10x + 15y. The company has 1200 labour-hours available, meaning they cannot exceed this limit. The constraint is 10x + 15y ≤ 1200 (labour-hours used is at most the available hours). An equation (=) fixes the exact usage, which is unnecessarily restrictive. A ≥ inequality suggests using more hours than available, which is infeasible.
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