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 $\ce{LPP}$ 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
$x_{11} ​+ x_{21} ​+ ..... + x_{m1} ​= b_{1​}$
$x_{12}​ + x_{22}​ + ..... + x_{m2}​ = b_{2​}$
$x_{1n}​ + x_{2n} ​+ ..... + xmn​ = b_n​$
$x_{11}​ + x_{12}​ + ..... + x_{1n}​ = b_1​$
$x_{21​}+ x_{22} ​+ ..... + x_{2n} ​= b_{2​}$
$x_{m1} + x_{m2}​ + ..... + x_{mn}​ = b_{n​}$
So the total number of constraints $= m + n$

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