MCQ
Minimise $\text{Z}=\sum\limits^{\text{n}}_{\text{j}=1}\sum\limits^{\text{m}}_{\text{i}=1}\text{c}_{\text{ij}}\cdot\text{x}_{\text{ij}}$ Subject to $\sum\limits^{\text{m}}_{\text{i}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,....\text{n}$ $\sum\limits^{\text{n}}_{\text{j}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,.....,\text{m}$ is a $\text{LPP}$ with number of constraints.
  • A
    $\text{m}-\text{n}$
  • B
    $\text{m}\text{n}$
  • $\text{m}+\text{n}$
  • D
    $\frac{\text{m}}{\text{n}}$

Answer

Correct option: C.
$\text{m}+\text{n}$
Constraints will be
$ x_{11}+x_{21}+\ldots \ldots+x_{m _1}=b_1 $
$ x_{12}+x_{22}+\ldots \ldots+x_{m_ 2}=b_2 $
$ x_{1_ n}+x_{2 n}+\ldots \ldots+x_{m_ n}=b_n $
$ x_{11}+x_{12}+\ldots \ldots+x_{1_ n}=b_1 $
$ x_{21}+x_{22}+\ldots \ldots+x_{2_ n}=b_2 $
$ x_{m _1}+x_{m _2}+\ldots \ldots+x_{m_ n}=b_n $
So the total number of constraints $= m + n$

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