Linear programming Flashcards
What is a decision variable?
A variable whose optimal quantity will be solved for
What is the objective function?
The function to either minimise or maximise, i.e. 3x+2y
What is a constraint?
A requirement that all feasible solutions must satisfy, i.e. no more than £x spent
What is a feasible solution?
A solution in which all decision variables satisfy each constraint
What is an optimal solution?
A feasible solution that has either minimised or maximised the objective function
How can a two variable linear programming problem be represented graphically?
By modelling the constraints as inequalities and then drawing these inequalities on a graph
In an inequality graph, how are strict inequalities represented?
With a dashed line
In an inequality graph, how are non-strict inequalities represented?
With a solid line
In an inequality graph, how is the feasible region represented?
It is the area left unshaded
What is an objective line?
A line with the equation n=O(x,y) where n is any number and O(x,y) is the objective function
Describe the objective line method
If the aim is to minimise the objective function, search for the first point in the feasible region that’s covered by an objective line (as it moves away from the origin). If the aim is to maximise the objective function, search for the last point that’s covered by an objective line.
Describe the vertex testing method
For all vertices in the feasible region, substitute the coordinate values into the objective function. Depending on whether the aim is to minimise or maximise the objective function, the optimal solution will be the values that produce either the lowest or highest result
How can one deal with a constraint requiring integer values only?
Find the optimal solution normally, and then check all surrounding integer values
