Matrices and Practical Problems

Data can usefully be summarised in a table, and a table can have it's borders, column and row labels taken away and then enclosed in brackets in which case it be come a matrix. Then we can perform useful calculations with it.

For instance:

The figures in the table show

The daily production, in kilograms, of two types,andof sweets from a small company,

The percentages of the ingredients A, B and C required to produceand


Percentages

Daily Production

(Kg)


A

B

C

60

30

10

300

50

40

10

240

Cost £ per Kg

4

6

8


Our task is to find the total cost of production

We can do this by changing the percentages into masses in Kg.

is 60%, 30%, 10% A, B, C respectively so the masses are 180, 90 and 30 Kg respectively.

is 50%, 40%, 10% A, B, C respectively so the masses are 120, 96 and 24 Kg respectively.

We can form a matrix representing the masses of ingredients used:

When we multiply this by the vector representing the costs of the ingredients we will get the cost of producing 300Kg ofand 240Kg ofrespectively.

Hence the total cost of production is £1500+£1248=£2748.