# Answer in Operations Research for Akki #243653

The problem is converted to canonical form by adding slack, surplus and artificial variables as appropriate

1. As the constraint-1 is of type ‘≤’ we should add slack variable “S_1”

2. As the constraint-2 is of type ‘≤’ we should add slack variable “S_2”

3. As the constraint-3 is of type ‘≤’ we should add slack variable “S_3”

4. As the constraint-4 is of type ‘≤’ we should add slack variable “S_4”

**After introducing slack variables**

“text{Max } z=4x_1+3x_2+0S_1+0S_2+0S_3+0S_4\ntext{Subject to }\n~~2x_1+x_2+S_1~~~~~~~~~~~~~~~~~~~~~~~~=1000\n~~~~x_1+x_2~~~~~~~~+S_2~~~~~~~~~~~~~~~~=800\n~~~~x_1~~~~~~~~~~~~~~~~~~~~~~~~~+S_3~~~~~~~~=400\n~~~~~~~~~~~~~x_2~~~~~~~~~~~~~~~~~~~~~~~~+S_4=700\ntext{All variables nonnegative}”

Negative minimum “z_j-c_j” is -4 and its column index is 1. So, the entering variable is “x_1” .

Minimum ratio is 400 and its row index is 3. So, the leaving basis variable is “S_3” .

∴ The pivot element is 1.

“R_3(new)=R_3(old), R_1(new)=R_1(old)-2R_3(new)\nR_2(new)=R_2(old)-R_3(new), R_4(new)=R_4(old)”

Negative minimum “z_j-c_j” is -3 and its column index is 2. So, the entering variable is “x_2” .

Minimum ratio is 200 and its row index is 1. So, the leaving basis variable is “S_1” .

∴ The pivot element is 1.

“R_1(new)=R_1(old), R_2(new)=R_2(old)-R_1(new)\nR_3(new)=R_3(old), R_4(new)=R_4(old)-R_1(new)”

Negative minimum “z_j-c_j” is -2 and its column index is 5. So, the entering variable is “S_3” .

Minimum ratio is 200 and its row index is 2. So, the leaving basis variable is “S_2” .

∴ The pivot element is 1.

“R_2(new)=R_2(old), R_1(new)=R_1(old)+2R_2(new)\nR_3(new)=R_3(old)-R_2(new), R_4(new)=R_4(old)-2R_2(new)”

Since all “z_j-c_jgeq0”

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

“x_1=200,x_2=600”

“Max~z=2600”