Minimize \[z=\sum\limits_{j=1}^{n}{{}}\sum\limits_{i=1}^{m}{{{c}_{ij}}\,{{x}_{ij}}}\] Subject to : \[\sum\limits_{j=1}^{n}{{{x}_{ij}}\le {{a}_{i}},\ i=1,.......,m}\] \[\sum\limits_{i=1}^{m}{{{x}_{ij}}={{b}_{j}},\ j=1,......,n}\] is a (L.P.P.) with number of constraints [MP PET 1999]

Minimize \[z=\sum\limits_{j=1}^{n}{{}}\sum\limits_{i=1}^{m}{{{c}_{ij}}

1.	Minimize \[z=\sum\limits_{j=1}^{n}{{}}\sum\limits_{i=1}^{m}{{{c}_{ij}}\,{{x}_{ij}}}\] Subject to : \[\sum\limits_{j=1}^{n}{{{x}_{ij}}\le {{a}_{i}},\ i=1,.......,m}\] \[\sum\limits_{i=1}^{m}{{{x}_{ij}}={{b}_{j}},\ j=1,......,n}\] is a (L.P.P.) with number of constraints [MP PET 1999]
A.	\[m+n\]
B.	\[m-n\]
C.	mn
D.	\[\frac{m}{n}\]
Answer» B. \[m-n\]

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Minimize \[z=\sum\limits_{j=1}^{n}{{}}\sum\limits_{i=1}^{m}{{{c}_{ij}}\,{{x}_{ij}}}\] Subject to : \[\sum\limits_{j=1}^{n}{{{x}_{ij}}\le {{a}_{i}},\ i=1,.......,m}\] \[\sum\limits_{i=1}^{m}{{{x}_{ij}}={{b}_{j}},\ j=1,......,n}\] is a (L.P.P.) with number of constraints [MP PET 1999]

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