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.
When we formulate the LPP from the above-given passage. Which of the following is an objective function for its dual problem?
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Show answer & explanation
Correct answer: B. Min P = 8u + 10v + 15w
Explanation
Primal: maximize 30x + 50y subject to 2x + 3y ≤ 8 (red), 3x + 2y ≤ 10 (green), 2y ≤ 15 (blue). The dual minimizes the right-hand sides weighted by dual variables: Min P = 8u + 10v + 15w.
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