Discrete Math Mr' Gilbert

1
Discrete MathMr. Gilbert

• Matrix Applications
• 7.1 The Leontief Input-Output Model
• Part 1 of 2

2
Essential Questions
1. How do you use matrices to organize,
manipulate, and display information? 2. How can
matrices be used to model real world phenomenon?
3
Students shall be able to

• Use directed graphs to model the flow of goods in
  the economy.

• Analyze relationships between sectors in the
  economy through a consumption matrix

4
Agenda

• Warm up
• Homework review
• Lesson / activity
• Class work
• Summary

5
Communicate Effectively

• Sectors of the economy A grouping of the economy
  by the type of activity or service performed.
• Consumption Matrix A simple way for a
  manufacturer to describe internal use of their
  product.
• Demand (D) The amount of product or service a
  company can sell.
• Total Production The amount of product that a
  company can make.

6
Sectors of the Economy in NAICS

• List data sets by sector
• 11 Agriculture, Fishing and Hunting 21 Mining
• 22 Utilities 23 Construction 31
  Manufacturing42 Wholesale Trade 44 Retail
  Trade48 Transportation and Warehousing 51
  Information
• 52 Finance and Insurance
• 53 Real Estate and Rental and Leasing54
  Professional, Scientific, and Technical
  Services55 Management of Companies and
  Enterprises56 Waste Management and Remediation
  Services61 Educational Services62 Health Care
  and Social Assistance71 Arts, Entertainment,
  and Recreation72 Accommodation and Food
  Services81 Other Services (Except Public
  Administration)

7
Math Term

• Digraph A graph with directed edges.
• Directed mean only traveling one direction A to
  B and A to B and B to B

8
Consumption Matrix

• Given
• For the battery division to produce 100 batteries
  it must use 3.
• For every 100 batteries produced 1 motor is
  required from the motor division
• For a motor division to produce 100 motors, it
  must use 4 (4) of its own motors.
• For every 100 motors produced, 8 batteries are
  required from the battery division.

9
Digraph From Consumption Matrix
0.08
0.04
0.03
B
M
0.01