Page 112 - DMTH201_Basic Mathematics-1

Unit 4: Determinants

units of X and 1 unit of Z. C purchases 1 unit of X and sells 4 units of Y and 6 units of Z. In the Notes
process A, B and C earn 6000, 5,000 and 13,000 respectively. Using matrices, find the prices of
the three commodities (note that selling the unit is positive earning and buying the units is
negative earning.)
Solutionl

The given information can be written as the following set of equations:

3x 5 – 4z 6,000 3 5 4 x 6,000
y
2 – 3y z 5,000 or 2 3 1 y 5,000
x
–x 4y 6z 13,000 1 4 6 z 13,000
Let A be the matrix of the coefficients

|A| = –54 – 5 – 32 + 12 – 12 – 60 = –151 0.
Writing the matrix of cofactors, we get

22 13 5 1 22 46 7
C = 46 14 17 A 1 13 14 11
7 11 19 151 5 17 19

x 22 46 7 6,000
1
Thus, y = 13 14 11 5,000
z 151 5 17 19 13,000

22 6,000 46 5,000 7 13,000
x = 3,000
151

13 6,000 14 5,000 11 13,000
y = 1,000
151
5 6,000 17 5,000 19 13,000
z = 2,000 .
151

Example
A company has two productions departments, P and P , and three service departments, S , S
1 2 1 2
and S . The direct cost allocated to each of the departments and the percentage of total cost of
3
each service department apportioned to various departments are given below:
Deptt. Direct Cost (Rs.) Percentage Allocation of Total Cost
S 1 S 2 S 3
P 1 60,000 40 35 25

P 2 74,000 20 40 20
S 1 6,000 0 20 35
S 2 8,000 15 0 20
S 3 68,500 25 5 0

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