Linear programming exercises Flashcards
If product x takes 5 machine and 10 labor hours while product y takes 15 machine hours and 5 labor hours while there are only 60 machine hours and 40 labor hours available how do you set up the constraints in linear programming
5x + 15y < 60
10x + 5y < 40
Does the simplex method accept nagative RHS varaibels
No!
Does the simplex method accept < or > constraints
No, only equalities so you have to put it in standard form
surplus variables are added to put the constraint in standard form
False, slack variables are added, surplus variables are subtracted in addition to an artificial variable with a coefficient of -M
How do you create the first row of the simplex tablau
When you have the linear programming constraints and objective function in standard form take the coefficients of the objective function and including 0 for the slack and surplus variables and -M for the artificial and put them in the first row.
How do you create the constrain rows in the simplex tablau
for the variable columns add the coefficients in the left hand side of the constraint coresponding to the variable and if a particular variable is not present in the left hand side add a 0. For the slack and artificial variables add a 1 if the slack is active (is in the constraint corespondind to the row) for that constraint and for surplus variables add a -1, if either is not active add a 0. For the first item in the row add the value of the slack or artificial variable that has 1 and for the last item in the row add the right hand side value of the constraint
How do you add a Zj row to the simplex tablau
The Zj value in a column is the sum of each constraint value in the same column although each value in the column is multiplied by the first item in their row. (Remember this first item coresponds to the item in the first row that has a 1 for the row that you want the first value of)
_89
810
901
How do you calculate the last row in the simplex tablua
You subtract the Zj value form the Cj(first row) value in each column
In standard for an artificial variable is added to = constraints
True
When iterating through simplex tablaus if the artificial variable is not basic, its entire column can be removed
True
When iterating through the simplex tablau how do you find the (pivot) key column
It is the column with the highest value in the Cj - Zj row
When iterating through the simplex tablau how do you find the (pivot) key row
Divide each item in the RHS column by the value in the key column on the same row. The key row is the one with the lowest positive number
When iterating through the simplex tablau how do you find the key (pivot) element
If you have the key row and the key column the pivot element is where they corss
When iterating through the simplex tablau how do you create a new key row in a new tablau
For each value in the pivot row of the old simplex tablau put old value divided by key element, in the new tablau in their coresponding places (where the old value was in the old tablau)
When iterating through the simplex tablau how do you create the none pivot constraint rows
For each value is the old value - (ckr - ckc)/ke where ke is the key element, ckr is the value in the key row on the same column as the old value and ckc is the value in the key column on the same row as the old value.
How do we know if we have an optimal solustion with the simplex method
If there are no positive values in the Cj-Zj row. If a surplus, slack or artificial value in the row is 0 there may be alternative solutions
How do you know if the problem is unbounded using the simplex method
If there are no positive RHS values when divided by key column
