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A mixture is to be made of three foods A, B, C. The three foods,A, B, C contain nutrients P, Q, R as shown below :  Gram per kg of nutrient

 P Q R
 A 1 2 5
 B 3 1 1
 C 4 2 1

How to from a mixture which will have 8 gram of P,5 gram of Q and 7 gram of R ?

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Let food needed by x kg of A, y kg of  B and z kg of C. Therefore x kg of A contains 1 gram of nutrient P. So x kg of A   will contain  x grams of nutrient P Similarly, the amount of nutrient P in y kg of food B and  z kg of food C are 3y and 4z grams respectively. So, total quantity of nutrient P in x kg of food A, y kg of food B and z kg of food C is x+ 3y + 4z gram.

x+3y+4z = 8

Similarly, 2x+y+2z = 5  and 5x+Y+z = 7

The above system of simultaneous linear equations can be written in matrix form as AX = B

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