Directions (Q91–95): A firm can produce two types of cloth, A and B. Three kinds of wool are required: red, green and blue. One unit length of type A cloth needs 2 yards of red and 3 yards of green wool. One unit length of type B cloth needs 3 yards of red wool, 2 yards of green wool and 2 yards of blue wool. The firm has a stock of only 8 yards of red wool, 10 yards of green wool and 15 yards of blue wool. The income from one unit length of type A and type B cloth is ₹30 and ₹50 respectively. Let x and y be the unit lengths of type A and type B cloth produced.
How many unit lengths of cloth A are used when income is maximised (as per the keyed answer)?
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Correct answer: C. 2.8 unit
Explanation
The keyed solution uses the intersection of 2x + 3y = 8 and 3x + 2y = 10, i.e. x = 2.8, y = 0.8, income ₹124. However, checking every corner of the feasible region shows the vertex (0, 8/3) gives 50 × 8/3 ≈ ₹133.3, which is higher. So strictly the optimum produces no cloth A; none of the options matches that, and the keyed answer is 2.8.More Discrete Structures and Optimisation questions
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