4. A dietitian in a hospital is to arrange a special diet using three foods, L,

Question

4. A dietitian in a hospital is to arrange a special diet using three foods, L, M, and N. Each ounce of food L contains 20 units of calcium, 10 units of iron, 10 units of vitamin A, and 20 units of cholesterol. Each ounce of food M contains 10 units of calcium, 10 units of iron, 15 units of vitamin A, and 24 units of cholesterol. Each ounce of food N contains 10 units of calcium, 10 units of iron, 10 units of vitamin A, and 18 units of cholesterol. If the minimum requirements are 300 units of calcium, 200 units of iron, and 240 units of vitamin A, how many ounces of each food should be used to meet the minimum requirements and at the same time minimize the cholesterol intake? What is the minimum cholesterol intake? o (

Explanation / Answer

20L + 10M + 10N >= 300 ---> Equation 1
10L + 10M + 10N >= 200 ---> Equation 2
10L + 15M + 10N >=240 ----> Equation 3
Cholestrol : 20L + 20M + 18N to be reduced

Solving Equation 2 and 3: we get M = 8

By substituting M=8 in equation 1 & equation 2

20L + 10N = 240

10L + 10N = 120

Solving the above 2 equations, we get L=12 & N=0.

12 ounces of Food L and 8 ounces of Food M.
Minimum cholesterol intake = 240 + 160 = 400 units.

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