Linear programming slides Flashcards
In linear programming both the constraints and the objective function is linear
True
When is a linear programme in standard form
when all the variables are non-negative and all the constraints are equalities
How do you attain standard form in linear programming
By adding slack values to lesser than constraints and subtracting surplus values from greater than constraints.
How do you center a moving average
You do a moving avarage on the moving averages if the number of periods moved is even the periods which lack value otherwise becomes more on one side than the other.
What are the steps to forecast with seasonal changes
First calculate the yearly moving average and center it, Then calculate the StIt by dividing the period value with the moving average. After that calculate the seasonal component by taking the average StIt for the season. Then calculate the scaled seasonal factor by dividing the seasonal component by the average seasonal component. After that you get the unseasoned value by dividing the original value with the scaled seasonal factor Yt/St. Lastly you can calculate a forecast using the Least Squared method and then multiplying with the seasonal compoent.
Slack and surplus variables represent the difference
between the left and right sides of the constraints.
True
Slack and surplus variables have objective function
coefficients equal to 1
False, in the objective function their coefficient is 0
When looking for the optimal solution in a linear program, you do not have to evaluate all feasible solution points
True, you only have to look at the extreme points
What is the right hand side value in linear programming
I belive they are the value on the right side of the constraint when they are in = form. The limits of the constraints
What is the reduced cost for a decision variable
The amount a variables objective function coefficient would have to improve to make the variable prositive. The reduced cost for a positive decition variable is 0
If there is no point that satisfies all constraints in a linear programming problem is it unbounded
No its infeasible
A linear program in standard form has no negative constraints and all variables are equalities
No vice versa, the variables are none negative and the constraints are equalities
What is a basic variable in the linear programming simplex method
when a variable whose coefficient in the equation is +1 and whose coefficient in all other equations of the problem is 0.
What is required to put a linear program in tablu form for the simplex method
All right hand side values for the constraints must be positive and there must be one basic variable
When setting up the simplex tablau if the problem is a minimization problem you should multiply the objective function by -1.
Yes
When setting up the simplex tablau you should multiply the constraint equation with -1 if the right hand side value is negative
True
When setting up the simplex tablau you should add slack variables to > constraint and remove surplus variables from < constraints
No the reverse, add slack variables to less than constraints and remove surplus values from greater than constraints
When setting up the simplex tablau you should add an artifiicial value to each constraint
True
When setting up the simplex tablau you should set each slack and surplus variable’s coefficient in the objective function equal to zero
True
When setting up the simplex tablau you should sett the artificial variables to a varry large positive number M in the objective funation
False M should be negaticve -M
What is the first step in the simplex method of solving linear programming problems
To determine the entering variable by identifiing the variable with the most positive value in the c-z row.
What is the pivot column in linear programming
The entering column with the entering value, the most positive in the c-z row
Wha is step two in the simplex method for solving linear programming problems
Determine Leaving Variable
– For each positive number in the entering column, compute
the ratio of the right-hand side values divided by these
entering column values.
– If there are no positive values in the entering column, STOP;
the problem is unbounded.
– Otherwise, select the variable with the minimal ratio. (The
leaving row is called the pivot row.)
What is step 4 of the simplex method
For each column j multiply the objective function coefficients of the basic values by the corresponding numbers in column j and sum them
What is step 5 of the simplex method
Subtract the z row from the c row gor each column j. If no values in the c-z tow are positive go bavk to step1. If the artificial value is positive the problem is infeasible. If any none basic value is 0 alternative solutions exhist otherwise you have found the solution
What values are in the c-z tow in the simplex tablu
The coefficients of the objective function
How do you detect infeasibility using the simplex method
When an artificial variable remains positive in the final tablau
How do you detect unboundedness using the simplex method
If all entries in an entering column are non positive
How do you detect alternative optimal solutions using the simplex method
If the final tablu has c-j values equaling 0 for a non basic variable
