Directions (Q91–95): Food X contains 6 units of vitamin D and 7 units of vitamin E per gram and costs ₹12 per gram. Food Y contains 8 units of vitamin D and 12 units of vitamin E per gram and costs ₹20 per gram. The daily minimum requirements of vitamins D and E are 100 units and 120 units. Let x and y be the grams of food X and Y.
Which of the following are quantities (in grams) of food X and Y respectively when the cost of food is minimum:
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Correct answer: B. 15 and 5/4
Explanation
Corners: (0, 12.5) costs 250; (120/7, 0) costs about 205.7; the intersection of 6x + 8y = 100 and 7x + 12y = 120 is x = 15, y = 1.25, costing 180 + 25 = 205 — the minimum.
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