6 - Linear Programming Flashcards
Define decision variables.
Numbers of each of the things which can be varied.
Define objective function.
An algebraic expression showing the main aim of the problem - minimise/maximise.
Define constraints.
Things which prevent you from making/using an infinite number of each of the variables - each one gives rise to one inequality.
Define feasible solution.
Values for the decision variable which satisfy each constraint.
Define feasible region.
Region in a graphical linear programming problem containing all of the feasible solutions.
Define optimal solution.
Feasible solution meeting the objective - may be more than one.
How do you formulate a problem as a linear programming problem?
.Define decision variables.
.State objective.
.Write inequalities for constraints.
.(Make assumptions e.g. all sold).
What sections are shaded in?
Ones which fail to satisfy the inequalities.
How do you find the solution?
Find the point in the feasible region that maximises/minimises the objective function.
How do you use the objective line/ruler method?
Draw an objective line. Slide the ruler parallel to this line and the last point it touches is the maximum value and first point for minimum value. Use set square.
How do you use the vertex testing method?
Solve the equations simultaneously and see if they give the max/min value.
What do you do if integer solutions are required?
Consider integer coordinates.
How do you find the integer solution?
.Look for the last integer solution covered by the objective line.
.Find optimal solution, test closest integer solutions, see if they lie in the feasible region and evaluate the objective function.
