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A nutritionist is designing a daily diet plan of a person using five food items: Milk, Spinach, Almonds, Oats, and Rice. The Minimum Daily Requirement (MDR) of the nutrients Calcium, Iron and Protein should be 1100 mg, 15 mg, and 40 g, respectively. The following table gives nutrient content per serving of each food item:
| Food item | Calcium (mg) | Iron (mg) | Protein (g) |
|---|---|---|---|
| Milk | 300 | 0 | 8 |
| Spinach | 90 | 6 | 3 |
| Almonds | 210 | 4 | 6 |
| Oats | 120 | 3 | 5 |
| Rice | 50 | 1 | 4 |
Each serving provides a certain percentage of the MDR. For example, one serving of milk satisfies 20% of MDR of Protein. Further, the number of servings of any food item should be a whole number.
If only $$x$$ servings of Milk and $$y$$ servings of Rice are included in the diet plan, then the minimum value of $$x + y$$ that will satisfy the MDR of all three nutrients is
From Iron: Milk contributes 0, so $$y \geq 15$$ (Rice provides 1 mg/serving, need ≥ 15).
From Calcium: $$300x + 50y \geq 1100$$. With $$y = 15$$: $$300x \geq 350 \Rightarrow x \geq 2$$.
Protein: $$8 \cdot 2 + 4 \cdot 15 = 76 \geq 40$$ ✓.
Min $$(x, y) = (2, 15)$$, so $$x + y = \mathbf{17}$$.
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