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.
On the basis of the available material, the maximum total income is:
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Correct answer: A. ₹133.3
Explanation
Corner points of the feasible region: (0, 0) → 0; (10/3, 0) → ₹100; (2.8, 0.8) → ₹124; (0, 8/3) → 50 × 8/3 ≈ ₹133.3. The maximum is ₹133.3 at x = 0, y = 8/3. (Some published keys give ₹124, which is only the value at the intersection point.)More Discrete Structures and Optimization questions
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