Linear programming, del 1

Question 1

Vad är linear programming?

Answer 1

En matematisk metod för att optimera ett linjärt mål (en viss kvantitet) under en uppsättning av linjära restriktioner

Question 2

What is the objective in all LP problems?

Answer 2

The objective = Målfunktionen

The maximization or minimization of en viss quantity.

Question 3

Vad finns det för olika sorters solutions?

Answer 3

Feasible, Optimal, Graphical

Question 4

Vad innebär de tre olika solutions?

Answer 4

A feasible solution satisfies all the problem’s constraints.

An optimal solution is a feasible solution that results in the largest possible objective function value when maximizing. (or smallest when minimizing)

A graphical solution method can be used to solve a linear programmed with two variables.

Question 5

Vad måste vara uppfyllt för att problemet ska vara linear programming problem?

Answer 5

Both the objective function (målfunktionen som vi vill maximera eller minimera) and the constraints must be linear.

Linear functions är function där varje variabel appears i en separat term raised to the first power and is multiplied by a constant (kan vara 0)

Linear constraints är linjära funktioner som är restricted to “less than or equal to ≤”, “equal to =”, or “greater than or equal to ≥”.

Question 6

Guidance for how to formulate the problem:

Answer 6

Understand the problem thoroughly.
Describe the objective.
Describe each constraint.
Define the decision variables.
Write the objective in terms of the decision variables.
Write the constraints in terms of the decision variables

Question 7

Vad innebär standard form?

Answer 7

Standard form is a linear programme in which all variables are positive and all constraints are equalities.

Att alla constraints är equalities innebär att de skrivs med = och inte något av de andra tecknen.

Question 8

How to reach standard form?

Answer 8

Add slack variables for constraints with ≤

Remove surplus variables for ≥

Question 9

What is extreme points?

Answer 9

Corners or vertices (hörn) of the feasible region are referred to as extreme points.

Question 10

Where can we find optimal solution to an LP problem?

Answer 10

Can be found at an extreme point of the feasible region.

Man behöver endast consider the extreme points of the feasible region, inte alla feasible solution points.