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If there are $m$ sources and $n$ destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is
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Verified Answer
The correct answer is:
$m+n-1$
If $x_{i j} \geq 0$, is the number of units shipped from $\mathrm{i}^{\text {th }}$ source to $\mathrm{j}^{\text {th }}$ destination, then the equivalent LPP model will be
Minimize $Z=\sum_{i=1}^m \sum_{j=1}^n c_{i j} x_{i j}$
Subjected to:
$\begin{aligned}
& \sum_{i=1}^m x_{i j} \leq b_i(\text { demand }) \\
& \sum_{j=1}^n x_{i j} \leq a_i(\text{supply})
\end{aligned}$
If total supply $=$ total demand then it is a balanced transportation problem otherwise it is called an unbalanced transportation problem.
There will be $(m+n-1)$ basic independent variables out of $(m \times n)$ variables.
Minimize $Z=\sum_{i=1}^m \sum_{j=1}^n c_{i j} x_{i j}$
Subjected to:
$\begin{aligned}
& \sum_{i=1}^m x_{i j} \leq b_i(\text { demand }) \\
& \sum_{j=1}^n x_{i j} \leq a_i(\text{supply})
\end{aligned}$
If total supply $=$ total demand then it is a balanced transportation problem otherwise it is called an unbalanced transportation problem.
There will be $(m+n-1)$ basic independent variables out of $(m \times n)$ variables.
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