Directions (Q91–95): Food X contains 6 units of vitamin D per gram and 7 units of vitamin E per gram and costs Rs 12 per gram. Food Y contains 8 units of vitamin D per gram and 12 units of vitamin E per gram and costs Rs 20 per gram. The daily minimum requirements of vitamin D and E are 100 units and 120 units respectively. Let x be the quantity (in grams) of food X and y the quantity (in grams) of food Y.
What are the quantities (in grams) of food X and Y respectively when the cost of food is minimum?
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: B. 15 and 5/4
Explanation
Corner points: (0, 12.5) gives cost 250; the intersection of 6x + 8y = 100 and 7x + 12y = 120 is (15, 1.25), cost 180 + 25 = 205; (120/7, 0) gives ≈ 205.7. The minimum is at x = 15, y = 5/4.More Discrete Structures and Optimization questions
- The dual of the formulated LPP is:
- The minimum cost of food is:
- Consider the universe of positive integers X = {n | 1 ≤ n ≤ 8}, proposition P = "n is an even integer", Q = "(3 ≤ n ≤ 7) ∧ (n ≠ 6)". The tr…
- Let (Z, +) denote the group of all integers under addition. Then the number of automorphisms of (Z, +) is
- Let R = {x | x ∈ N, x is a multiple of 3 and x ≤ 100} and S = {x | x ∈ N, x is a multiple of 5 and x < 100}. What is the number of elements…
- There are m points on one straight line AB and n points on another straight line AC, none of them being A. How many triangles can be formed…