The chief materials used in the manufacture of three carpets designs called 'Floral Dance',

'Blue Danube' and 'Square Peg' are wool and acrilan.

The numbers in matrix below give the quantities of wool and acrilan, and the labour and machine times required, for each unit broadloom length of carpet type.

Machine Wool Acrilan Labour time hr hr Floral dance 1.0 2.0 0.7 1.0 Blue Danube 0.5 2.4 0.6 0.9 Square Peg 1.2 1.5 0.5 1 .1 The quantities of wool and acrilan are given in 10 kg units. It has been proposed that the design of these three carpets be slightly changed, but the names retained. The extra amounts of wool, acrilan, and the times required, will be as follows:

Machine Wool Acrilan Labour time hr hr Floral Dance +0.2 -0.2 +0.1 +0.1 Blue Danube 1 +0.01 +0.1 -0.2 Square Peg +0.1 -0.2 +0.2 +0.2 The production and transportation cost per unit of each resource is:
Wool Acrilan Labour Machine time REQUIRED:
COST Production transport $
40 20 2 10 $
10 20 0 0 37

(a) How would matrix addition and multiplication be used to find total production and total transportation costs for each of the new carpet types?
Determine these costs from your matrix operations only

(b) Assume that the carpet manufacturers have decided to produce 200 new 'Floral Dance', 300 new 'Blue Danube' and 100 'New Square Peg' units of broadloom carpet length What matrix calculation(s) would produce the carpet manufacturer's total requirement for each of the inputs?
Determine these requirements

(c) Matrices are use in input-output analysis Give the relevant equation which relates the total output to the final demand. Describe briefly the constituent elements of each matrix used