Consider the following LPP:
$\begin{array}{ll} \text{Min.} Z= & x_{1}+x_{2}+x_{3} \\ \text{Subject to } & 3x_{1}+4x_{3}\leq 5 \\ & 5x_{1}+x_{2}+6x_{3}=7 \\ & 8x_{1}+9x_{3}\geq 2, \\ &x_{1},x_{2},x_{3} \geq 0 \end{array}$
The standard form of this LPP shall be:
- $\begin{array}{ll} \text{Min.}Z= & x_{1}+x_{2}+x_{3}+0x_{4}+0x_{5}\\ \text{Subject to} & 3x_{1}+4x_{3}+x_{4}=5;\\ & 5x_{1}+x_{2}+6x_{3}=7;\\ & 8x_{1}+9x_{3}-x_{5} = 2; \\ & x_{1},x_{2},x_{3},x_{4},x_{5}\geq 0 \end{array}\\$
- $\begin{array}{ll} \text{Min.}Z= & x_{1}+x_{2}+x_{3}+0x_{4}+0x_{5}-1(x_{6})-1(x_{7})\\ \text{Subject to} & 3x_{1}+4x_{3}+x_{4}= 5;\\ & 5x_{1}+x_{2}+6x_{3}+x_{6}=7;\\ & 8x_{1}+9x_{3}-x_{5}+x_{7}= 2;\\ & x_{1}\ \text{to} \ x_{7}\geq 0 \end{array}$
- $\begin{array}{ll} \text{Min.}Z= & x_{1}+x_{2}+x_{3}+0x_{4}+0x_{5}+0x_{6} \\ \text{Subject to} & 3x_{1}+4x_{3}+x_{4}=5;\\ & 5x_{1}+x_{2}+6x_{3}=7;\\ &8x_{1}+9x_{3}-x_{5}+x_{6} =2;\\ &x_{1}\ \text{to}\ x_{6}\geq 0 \end {array}\\$
- $\begin{array}{ll} \text{Min.}Z= & x_{1}+x_{2}+x_{3}+ 0x_{4}+ 0x_{5}+ 0x_{6}+ 0x_{7}\\ \text{Subject to} & 3x_{1}+4x_{3}+x_{4}=5;\\ & 5x_{1}+x_{2}+6x_{3}+x_{6}=7\\ & 8x_{1}+9x_{3}-x_{5}+x_{7}= 2; \\ & x_{1}\ \text{to} \ x_{7} \geq 0 \end{array}$