Food X contains 6 units of Vitamin D per gram and 7 units of Vitamin E per gram and cost is Rs 12 per…
For a primal problem "minimise \(c^T x\) subject to \(Ax \ge b\), \(x \ge 0\)", the dual is "maximise \(b^T u\) subject to \(A^T u \le c\), \(u \ge 0\)". Here b = (100, 120)…
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Food X contains 6 units of Vitamin D per gram and 7 units of Vitamin E per gram and cost is Rs 12 per gram. Food Y contains 8 units of vitamin D per gram and 12 units of Vitamin E per gram and cost is Rs 20 per gram. The daily minimum requirements of vitamin D and E are 100 units and 120 units respectively. Suppose x is quantity (in gram) of food X, y is quantity (in gram) of food Y. Answering the following question based on the above paragraph given.
The dual of the formulated LPP is :
Answer and explanation
Correct answer A
For a primal problem "minimise subject to , ", the dual is "maximise subject to , ". Here b = (100, 120) and c = (12, 20), and the columns of the primal give and , with . The dual optimum u = 1/4, v = 3/2 gives , equal to the primal minimum, which confirms the formulation; unrestricted dual variables or ≥ constraints do not fit this primal.
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UGC NET Computer Science and Applications