Question

Solve the following linear program using simplex algorithm: Minimize z=a + b + c
Subject to 1. a-b-c 0
2. a + b + c 4
3. a + b - c= 2
4. a,b 0

Answer 1

Problem formulating as,

Minimize

$\quad z=a+b+c\\ subject\ to,\\ a-b-c\le 0\\ a+b+c\ge4\\ a+b-c=2\\$

After converting the simplex method(big M) form,

Minimize

$\quad z=a+b+c+0s_1+0s_2+MA_1+MA_2\\ subject\ to,\\ a-b-c+s_1= 0\\ a+b+c-s_2+A_1=4\\ a+b-c+A_2=2\\$

Steps of every table is described after all the tables.

$S_1$​ has gone out from the basis and a has come in to basis.

since all the $Z-C_j\le0$ , optimal answer is occurred.

Answer to the minimization problem is,

$\red{a=2\\b=1\\c=1\\Z_{min}=4\\}$ .