Food X contains 6 units of Vitamin D per gram and 7 units of Vitamin E per…
2023
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 cost funtion of total food is :
- A.
\(Z = 6x + 7y \) - B.
\(Z = 8x + 12y \) - C.
\(Z = 12x + 20y \) - D.
\(Z = 20x + 12y \)
Attempted by 33 students.
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Correct answer: C
Answer: The total cost function is Z = 12x + 20y.
Food X costs Rs 12 per gram, so x grams cost 12x rupees.
Food Y costs Rs 20 per gram, so y grams cost 20y rupees.
Total cost is the sum of these contributions: Z = 12x + 20y.
For completeness, the vitamin requirement constraints from the problem are:
Vitamin D requirement: 6x + 8y ≥ 100
Vitamin E requirement: 7x + 12y ≥ 120
Non-negativity: x ≥ 0, y ≥ 0