Linear Programming - Graphical Method Flashcards
Who invented the technique for optimizing shipping resources?
American mathematicians during World War 2.
What did George B. Dantzig develop from 1946 to 1947?
General linear programming formulation for planning problems in the US Air Force.
What significant method did Dantzig invent in 1947?
The simplex method.
What problem did the simplex method efficiently tackle?
Linear programming problem
When was linear programming published?
After WW2
Why was linear programming published after the war?
Due to the fear of Americans that other countries might take advantage of their method.
Main use of linear programming today?
Business models.
A method for solving problems in which a quantity is to be maximized or minimized when the quantity is subject to various restrictions or constraints.
Linear programming
When do linear programming problems arise?
In situations where available resources are limited or cannot be utilized completely.
When did George B. Dantzig develop general linear programming formulation
from 1946 to 1947
The optimal value of a linear function which defines the objectives of the problem subject to a set of linear constraints.
LP problem
The limit or decision environment of the problem.
Constraints
May mean maximizing profit or minimizing cost in a specific context.
Optimal
There must be a linear relationship between variables and constraints.
first property
The linear programming model should have an objective function.
second property
What is the third property of a linear programming model?
There must be structural constraints in the linear programming model.
Non-negativity constraints must be present in the linear programming model.
fourth property
There must be a _____ relationship between ____ and ____.
linear, variables, constraints
The linear programming model should have an?
Objective function.
There must be _______ in the linear programming model.
structural constraints
________ must be present in the linear programming model.
Non-negativity constraints
What are the 4 basic assumptions of a linear programming problem
- Proportionality
- Additivity
- Divisibility
- Certainty
The contribution of individual variables in the
objective function is proportional to their value.
Proportionality
The total value of the objective function and each
constraint is the sum of the individual contributions
from each variable.
Additivity
The decision variables can take on any real
numerical values within a specified range.
Divisibility
The parameters are known.
Certainty
What are 2 ways of solving a linear programming problem
- Graphical Method
- Simplex Method
The best used only for simple LP models involving two or three variables.
Graphical Method
LP models involving several decision variables.
Simplex Method
