Directions (Q91–95): A firm produces two types of cloth, A and B, using red, green and blue wool. One unit length of type A needs 2 yards of red and 3 yards of green wool. One unit length of type B needs 3 yards of red, 2 yards of green and 2 yards of blue wool. The firm has 8 yards of red, 10 yards of green and 15 yards of blue wool. Income is ₹30 per unit length of type A and ₹50 per unit length of type B.
How many unit length used for cloth A when income is maximized ?
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: C. 2.8 unit
Explanation
The red and green constraints 2x + 3y = 8 and 3x + 2y = 10 meet at x = 2.8, y = 0.8, which is what the official key uses.
Note: no option is fully correct; the official key (C) is shown. Corner points: (0, 8/3) gives ₹133.3, (2.8, 0.8) gives ₹124, (10/3, 0) gives ₹100. The true optimum uses x = 0, which is not an option; the official key 2.8 is the intersection of the red and green constraints.
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