MTH601 Final Term Practice Questions Solution Lectures 23-41

Maximization:

1. Objective function is of maximization type.
2. Inequalities are of ≤ type.
3. Slack variables are added to convert inequality into an equation.

Minimization:

1. Objective function is of minimization type.
2. Inequalities are of ≥ type.
3. Slack variables are subtracted and artificial variables are added to convert inequalities into an equation.

var Maximize Z x x x

x x S x x S x x x S S Setting x x x S S iable is ze deg ro hence the given solution is enearte ,A ,A

of the basic variable is Maximize Z x x x

x x A x x A x x x Setting x x x A A One zero in the initial stage,so it is degenerate basic solution.

x1 · x2 · S1 · S2 · S3 · Solution

Z

x2

-1/2

x1

-1/8

S3

-2 Solution is temporarily degenerate

Tie between S2 and S3

Z · x1 · x2 · S1 · S2 · S3 · RHS

-2

S1 · x2 · S3

-1

Z · x1 · x2 · S1 · S2 · S3 · RHS · S1

-1

x2

x1

-1

Basic variable x is equal to zero .This implies degenerate optimal solution. x = x x x = x x 2(x x ) 3(x x ) 0. 0. 0.

-x +x 2x 2x x -x x x x -x 3x 3x Taking x =x x x Z S S S s t S S S

S S S

Z · x1 · x2 · S1 · S2 · A · RHS

-3-M -4-2M M -12M

S1

A

-1

Z · x1 · x2 · S1 · S2 · A · RHS

M+1 4+2M M 4M+16

x2

A

-3 -2 -1

We cannot proceed further with maximization as there is no negative coefficient in the objective row but the final solution has the artificial variable in the basis with the value equal to 4.Hence the problem has no feasible optimal solution.