Linear programming A2-5 Flashcards
What is the objective of basic linear programming
Minimization or maximization of some quantity
What is a decision variable
A variable that management can controle the value of
What are the three key assumptions required for linear programming to be apropriate
proportionality, adativity and divisibility of the variables. Aka that you can count, compare and use them in math
What are the seven steps for graphically solving a two variable linear programming problem
- Draw pheasibility horizons for the constraints, 2. determine the horizon that is not stopped by any constraint, 3. chose a variable for the objective function. 4. Draw a line on the graph showing all combinations that returns the chosen variable. 5. extend that line untill it tangents the pheasibility fronteir. 6. Aproximate the value at the tangent. 7. confirm the solution point mathematically.
What is the standard form of a linear programme
When it is written in a form with all constraints written as equalities
What is a redundant constraint
A constraint that does not effect the fheasibility fronteir becouse it is to high
What are slack variables in linear programming
Variables that represents idle capacity
Slack variables are zero in the objective function of linear programming, why or why not
Yes they are zero normally to represent that slack variables do not effect decision making however they do ocasionally as unused assets can be sold.
Why should you save redundant constraints
Becouse they might be bonding later when technollogy or other conditions change
What are extereme points in linear programming
Sharp corneres in the feasibility fronteir, the optimal solution is at one of those points
What is a surplus variable
The oposite of slack variables
Can there be more than one optimal solution in linear programming
Yes if the objective function is pararell with the most extreme constraint line
What is an unbounded problem in linear programming
When production is unconstrained usually becouse some constraint is omitted resulting in the optimal production value being infinite
Can changeing the objective function help with infeasibility in linear programming
No, infeasibility is the result of to tight constraints
Can changeing the objective function help with an unbounded problem in linear programming
Sometimes
A binding constraint has no slack or surplus at the optimal solution
True
What is the range of opurtunity of variables in the objective function in linear programming
The degree each variable in the objective function can change without changing the optimal solution. Graphically it is the degree the objective function line can rotate on the optimal extreme point without getting stopped by the pheasibility fronteir
What is the goal of data envelopment
To indentiying operating units that are relatively inefficient
What is the dual price
The change in the value of the optimal solution per unit increase in the right hand (improvement) side of a constraint. F.ex how much an extra hour of overtime is worth.
What is the difference between shadow price and dual price
They are the same in maximization problems but shadow is negative in minimization problems.
What is the range of feasibility
The ranges of the constraint within which the shadow price does not change for the objective function
What is the 100% rule for objective function coefficients
If the sum of the percentage changes in coefficients are lower than 100% than the optimal solution does not change
What is the 100% rule for the constraint right hand side
For all the right hand sides, sum the percentage changes of the allowable increases and decreases, if the sum of percentages does not change then the dual value will not change
Should sunk costs be reflected in the objective function
No
Degeneracy occurs when the dual price equals zero for one of the binding constraints
True
In the case of degeneracy changes beyond the end point of the range of optimality will not nececitate re solving the linear programming problem
False
The 100% rule applies when there are changes in both the objective funtion and the right hand side of the coefficients at the same time
No, in that case it has to be recalibrated
If the cost is sunk then the dual price becomes the maximum premium that a firm would be willing to pay for a resource
False, that is true for relevant costs, for sunk costs the dual price is the amount a firm is willing to pay for another unit
Linear programming can be used for make or buy decisions
True
Linear programming can be used for production scheduling
True
Ending inventory aproximates the average inventory durring the month in production scheduling linear programming
That is a common assumption
Linear programming can be used for blending, diet and feed mix problems
True
A matrix cannot be used to define the decision variables in a blending problem
False, it is convenitnt to use a matri with collumns as final prodicts and rows as raw materials.
Does the need for values to be integers complicate linear programming problems
Yes although if the numbers are large it matters little
In data envelopment can a operating unit that excells in one aspect but fails in others be judged as relatively inefficient
No, for some reason
Explain the simplex method for solving linear programming problems
Compare the extreme points algebraically untill you find the optimal one.
What is a tableau
A matrix where the columns are objective function coeffocents, rows are the the value of the constraint. This creates a matrix where the rows and collumns are labled.
When should you use the simplex method instead of the graphical in linear programming
When you have more than two variables.
When do you need to introduce an atrificial variable in the simplex method for linear programming
When you have a greater than or equal to constraint
The constraint values on the righthand side of the constraint in a linear programming tableau can be negative
False
