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.
Which of the following constrains when formulating the LPP ?
- A.
\(6x + 7y \leq 100, 8x +12y \leq 120, x,y \geq 0\) - B.
\(6x + 7y \leq 100, 7x +12y \leq 120, x,y \geq 0\) - C.
\(6x + 7y \geq 100, 8x +12y \geq 120, x,y \geq 0\) - D.
\(6x + 8y \geq 100, 7x +12y \geq 120, x,y \geq 0\)
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Correct answer: D
Decision variables: Let x be grams of Food X and y be grams of Food Y consumed daily.
Vitamin D constraint: 6x + 8y >= 100
Vitamin E constraint: 7x + 12y >= 120
Non-negativity: x >= 0, y >= 0
Explanation: The daily requirements are minimum amounts, so each nutrient total must be at least the required value, which is why the inequalities are ">=". Coefficients come from units per gram of each food: Food X provides 6 units of D and 7 units of E per gram, and Food Y provides 8 units of D and 12 units of E per gram.
Note: If an objective function is needed (e.g., minimize cost), the cost in rupees would be 12x + 20y, but the question only asked for the constraints.