Question

Minimize $z = \sum_{j = 1}^{n}{\sum_{i = 1}^{m}{c_{ij}x_{ij}}}$

Subject to :$\sum_{j = 1}^{n}x_{ij} \leq a_{i},i = 1........,m$;$\sum_{i = 1}^{m}{x_{ij} = b_{j},j = 1......,n}$ is a LPP with number of constraints

• A. $m + n$
• B. $m - n$
• C. $mn$
• D. $\frac{m}{n}$

Answer 1

Answer: (A)

$m + n$

Answer 2

(I) Condition, $i = 1,x_{11} + x_{12} + x_{13} + ........... + x_{1n} \leq a_{1}$

$i = 2,x_{21} + x_{22} + x_{23} + ........... + x_{2n} \leq a_{2}$ $i = 3,x_{31} + x_{32} + x_{33} + ............ + x_{3n} \leq a_{3}$.........................

$i = m,x_{m1} + x_{m2} + x_{m3} + ........... + x_{mn} \leq a_{m} \rightarrow m\text{constraints}$ (II) Condition $j = 1,x_{11} + x_{21} + x_{31} + .......... + x_{m1} = b_{1}$

$j = 2,x_{12} + x_{22} + x_{32} + ........... + x_{m2} = b_{2}$........................

$j = n,x_{1n} + x_{2n} + x_{3n} + .............. + x_{mn} = b_{n} \rightarrow n$constraints

∴ Total constraints $= m + n$.