Question

There are three types of foods, Food 1, Food II, Food III.
Food I contains 1 unit of each of the nutrients A. B and
C. Food II contains 1 unit of nutrient A. 2 units of nutrient
B and 3 units of nutrient C. Food III contains 1. 3 and 4
units of nutrients A, B and C respectively. 7 units of A, 16
units of B and 22 units of nutrient C are required. Find the
units of three foods that will provide exactly these amounts.
Use matrix method.​

Answer 1

Given :  There are three types of foods, Food 1, Food II, Food III.  Food I contains 1 unit of each of the nutrients A. B and  C. Food II contains 1 unit of nutrient A. 2 units of nutrient  B and 3 units of nutrient C. Food III contains 1. 3 and 4  units of nutrients A, B and C respectively. 7 units of A, 16  units of B and 22 units of nutrient C are required.

To find : units of three foods that will provide exactly these amounts.

Solution:

Food 1  = X

Food 2 = Y

Food 3  = Z

X  +  Y +  Z    = 7     Eq1

X  + 2Y + 3Z  = 16    Eq2

X  + 3Y + 4Z  = 22   Eq3

Eq3 - Eq2  

=> Y + Z = 6

=> X + 6 = 7

=> X  = 1  

1 + 2Y + 3Z = 16

=> 2Y + 3Z = 15

Y + Z = 6

=> 2Y + 2Z = 12

=> Z = 3

    Y = 3  

                                         A         B       C

Food 1 =  1 Units               1           1         1

Food 2 = 3 Units              3         6         9

Food 3  = 3 units              3         9       12

    Total   7 units              7         16       22

Food 1 =  1 Units       , Food 2 = 3 Units     & Food 3  = 3 units  

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