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 44

If two servings of Milk are part of the daily diet plan, then the minimum number of servings of any other single item that can satisfy the MDR of all three nutrients is

Solution

Two servings of Milk give: Ca 600, Fe 0, P 16. Need remaining: Ca ≥ 500, Fe ≥ 15, P ≥ 24.

Min servings $$s$$ of each item alone:

Spinach (90, 6, 3): $$s \geq \max(\lceil 500/90 \rceil, \lceil 15/6 \rceil, \lceil 24/3 \rceil) = \max(6, 3, 8) = 8$$.
Almonds (210, 4, 6): $$\max(\lceil 500/210 \rceil, \lceil 15/4 \rceil, \lceil 24/6 \rceil) = \max(3, 4, 4) = \mathbf{4}$$.
Oats (120, 3, 5): $$\max(5, 5, 5) = 5$$.
Rice (50, 1, 4): $$\max(10, 15, 6) = 15$$.

Minimum is 4 servings of Almonds.

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If two servings of Milk are part of the daily diet plan, then the minimum number of servings of any other single item that can satisfy the MDR of all three nutrients is

Solution

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