Answer to Question #261271 in Operations Research for Ninu

Question

The following statement are tru or false? Give a short proof or a example your answer

The ptimal solution for the following LPPis z*30

Maxz= x1-x2+3x3

Subject to x1+x2+x3<=, 10

X1, x2, x3>=0

Answer 1

true

$Z_{max}=x_1-x_2+3x_3$

Solve by simplex method using online calculator:

$Z_{max}=30,x_1=x_2=0,x_3=10$

After introducing slack variables

Max Z=x1-x2+3x3+0S1

subject to

x1+x2+x3+S1=10

and x1,x2,x3,S1≥0

after Iteration-1:

Negative minimum Zj-Cj is -3 and its column index is 3. So, the entering variable is x3.

Minimum ratio is 10 and its row index is 1. So, the leaving basis variable is S1.

∴ The pivot element is 1.

Entering =x3, Departing =S1, Key Element =1

after Iteration-2:

Since all Zj-Cj≥0

Hence, optimal solution is arrived with value of variables as :

x1=0,x2=0,x3=10

Max Z=30