1
Q
What are slack variables used for?
A
They are added to variable inequalities to turn them into equations. They are also non-negative.
2
Q
What is the function of the simplex algorithm?
A
Determines whether a vertex is optimal, and which vertex should be moved to next.
3
Q
Describe the use of the one-way simplex algorithm to maximise.
A
- Draw table, Basic volumn on left, one column of each variable, value column, row operation column, R value column
One row for each constraint and one row for objective function. - Find most negative entry in objective row and label this column as pivot
- Divide value column by term in pivot column to get R value
- Select smallest R value to make that term (smallest R value and pivot column) the pivot
- Divide pivot row by pivot and chnage basic variable on left to variable at top of column
- use new pivot row to make the pivot colummn 0 in all other rows
- repeat steps 2-6 until there are no negative numbers in objective function
- now optimal
4
Q
What are surplus variables?
A
used to turn greater than inequalities into equations by subtracting a surplus variable and adding an articficial variable
5
Q
how to carry out two stage simplex
A
- use artifical +surplus variables
- let I = sum of artificial;s
- replace I with normal variables
- find I +- all variables = a constant value
- use simplex as normal
- if sum of artificals = 0, then use this solution to start the second iteration of simplex
- if != 0, no feasible solution to original problem
6
Q
big M
A
- use slack for >=
- use surplus + artificials for <=
- for each artifical, subtract M(a1 + a2 +a3) from objectiev
- write artificals in terms of normal variables
- simplex like normal
M is abitrily large
