Q. 11

# A company produces three products every day. Their production on a certain day is 45 tons. It is found that the production of the third product exceeds the production of a first product by 8 tons while the total production of a first and third product is twice the production of the second product. Determine the production level of each product using the matrix method.

Let the numbers are x, y, z

x + y + z = 45 ……(i)

Also,

Z – x = 8 ……(ii)

Again,

x + z = 2y …… (iii) A X = B

|A| = 1(2) – 1(– 2) + 1(2)

= 6

Hence, the unique solution given by x = A – 1B

C11 = (– 1)1 + 1 (0 + 2) = 2

C12 = (– 1)1 + 2 (– 1 – 1) = 2

C13 = (– 1)1 + 3 (2 – 0) = 2

C21 = (– 1)2 + 1 (1 + 2) = – 3

C22 = (– 1)2 + 2 (1 – 1) = 0

C23 = (– 1)2 + 3 (– 2 – 1 ) = 3

C31 = (– 1)3 + 1 (1 – 0) = 1

C32 = (– 1)3 + 2 (1 + 1) = – 2

C33 = (– 1)3 + 3 (0 + 1) = 1

X = A – 1 B = Adj A = X = X =  = Hence, x = 11, y = 15 and z = 19

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