Basic Maths:

Tutorial 6
Questions for in-class tutorial:
Basic Maths:

  1. Use the inverse matrix method to solve the given system of equations (note: use the Gauss-Jordan elimination method to find the inverse matrix)

x + z = 12
2x + 2y + z = 8
x + y – z = 2
Application Questions:

  1. Given the input/output table for the three-sector economy:
Input to
A B C Other demands Total output
Output from A 200 100 200 500 1000
B 100 0 500 200 800
C 100 80 0 620 800

 Calculate the total output required from each industry when other demands change to 400, 400, 1000 from sectors A, B and C, respectively.
 Given the matrix of technical coefficients, A, and final demand (other demand) B for industries 1, 2, and 3
A = , B =

  1. Determine (I – A)-1
  2. Calculate the total output required from each sector

 The technology matrix for an economy based on energy (E) and transportation (T) is
Find the output for each sector that is needed to satisfy a final demand of $50 million for energy and $50 million for transportation.
Questions for self-study
 A supplier manufactures car and truck frames at two different plants. The production rates (in frames per hour) for each plant are given in the table:
 

Plant Car Frames Truck Frames
A 10 5
B 8 8
  • How many hours should each plant be scheduled to operate to exactly fill 3000 car frames and 1600 truck frames?
  1. An economy is based on two industrial sectors, coal and steel. Production of a dollar’s worth of coal requires an input of $0.10 from the coal sector and $0.20 from the steel sector. Production of a dollar’s worth of steel requires an input of $0.20 from the coal sector and $0.40 from the steel sector. Find the output for each sector that is needed to satisfy a final demand of $20 billion for coal and $10 billion for steel.
  2. The input/output table for an organic farm is given as:
Input to
Hortic. Dairy Poultry Other demands Total output
Hortic. 50 40 200 210 500
Output from Dairy 100 160 0 140 400
Paultry 200 0 80 520 800
  1. a) Write down the matrix of technical coefficients
  2. b) Calculate the total output required from each section when other demands change to

200, 800, 1000 from horticulture, dairy and poultry sections, respectively
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