Discrete Mathematics
Lesson 7.1: Leontif Input-Output Model
1 Sector Economy
Consider the Best Battery Company: For every 100 batteries they produce, 3 or 3% are used within the company.
If the company produces 500 batteries, how many will be used within the company?
How many will be available for external sales?
P = total production by company
0.03P = batteries used internally
= batteries available for external sales (demand, D)
How many batteries must the company produce to meet an external demand (order) of 5000 batteries?
Therefore, the company needs to produce ______batteries to meet an order of 5000.
2 Sector Economy
Now the Best Battery Company buys an electric motor company and begins producing motors as well as batteries. Now the company has two divisions, the battery division and the motor division. The production requirements are as follows:
Battery Division
- For the battery division to produce 100 batteries, it must use 3 (3%) of its own batteries.
- For every 100 batteries produces, 1 motor (1% of the number of batteries produced) is required from the motor company.
Motor Division
- For the 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. (8% of the total number of motors produced)
Production needs can be represented using a weighted digraph.
Another way to represent a company’s production needs is with a consumption matrix.
To
Battery Motor
How many batteries and motors will be used internally to produce 200 batteries?
Battery division needs 3% of their own batteries and 1% of the motors.
How many batteries and motors will be used internally to produce 100 motors?
Explore This: The company has given the battery division a daily total production quota of 1000 batteries. The daily quota for the motor division is 200 motors. Determine how many batteries and motors each of the company’s divisions will need during production and how many will be available for sales.