Instructions

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.

Question 45

The food item(s) that can satisfy at least half of the MDR for all the three nutrients using up to seven servings of that single item alone is

Solution

50% MDR thresholds: Ca ≥ 550, Fe ≥ 7.5, P ≥ 20. Try each item alone with up to 7 servings:

Milk: Iron is 0, never reaches 7.5. ✗
Spinach (90, 6, 3): need $$\lceil 550/90 \rceil = 7$$, $$\lceil 7.5/6 \rceil = 2$$, $$\lceil 20/3 \rceil = 7$$. Min = 7 ≤ 7. ✓
Almonds (210, 4, 6): need $$\lceil 550/210 \rceil = 3$$, $$\lceil 7.5/4 \rceil = 2$$, $$\lceil 20/6 \rceil = 4$$. Min = 4. ✓
Oats (120, 3, 5): need $$\lceil 550/120 \rceil = 5$$, $$\lceil 7.5/3 \rceil = 3$$, $$\lceil 20/5 \rceil = 4$$. Min = 5. ✓
Rice: Ca $$\geq 550$$ needs 11 servings. ✗

Only Almonds, Spinach, and Oats.

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The food item(s) that can satisfy at least half of the MDR for all the three nutrients using up to seven servings of that single item alone is

Solution

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