Question

Max Z = 2x1 + 8x2 + 4x3

subject to

2x1 + 3x2     ≤ 8

2x2 + 5x3     ≤ 12

3x1 + x2 + 4x3         ≤15

and x1,x2,x3≥0;

Indicate clearly the optimal basic and nonbasic variables and their values and write the reduced cost of each optimal nonbasic variable.

Answer 1

step 1- convert above inequality into an equation by adding slag variable( less than equal is given)

step-2 construct the table corresponding to a basic solution

• Cb= coefficient of a basic variable in the objective function
• Cj= contribution of variables in objective function
• B=basic variable
• optimality condition all Cj-Zj<=0
• MPR= minimum positive ratio( b(column)/ key column)

INTERPRETATION-

NON BASIC VARIABLE- variable(X1,X2,X3) that we put =0 for solving basic variable(S1, S2, , S3) , values of non basic variable are-

x1=0 i.e it is not produced

x2= 8/3

x3= 4/3

maxz= 2*0+8*(8/3)+4*(4/3)

= (64/3)+ (16/3)

= 80/3

as it is optimal so it cant increase to (80/3)

NOTE- IF YOU BLIKE MY ANSWER GIVE ME THUMBS UP, IT KEEPS MOTIVATING ME, THANX