Draw the Network Representation of the Following Network Flow Problem

question 62

Essay

Draw the network representation of the following network flow problem.
MIN: $\begin{array} { l } 5 \mathbf { X } _ { 1 \mathbf { 4 } } + 3 \mathbf { X } _ { 1 \mathbf { 3 } } + 2 \mathbf { X } _ { 14 } + 3 \mathbf { X } _ { \mathbf { 4 4 } } + 2 \mathbf { X } _ { \mathbf { 3 4 } } \\\end{array}$
Subject to:
$\begin{array} { l } - \mathbf { X } _ { 1 \mathbf { 1 } } - \mathbf { X } _ { 1 \mathbf { 1 } } - \mathbf { X } _ { 14 } = - 10 \\\mathbf { X } _ { 1 \mathbf { 2 } } - \mathbf { X } _ { \mathbf { 2 4 } } = \mathbf { 2 } \\\mathbf { X } _ { 1 \mathbf { 3 } } - \mathbf { X } _ { \mathbf { 3 4 } } = \mathbf { 3 } \\\mathbf { X } _ { 14 } + \mathbf { X } _ { \mathbf { 2 4 } } + \mathbf { X } _ { \mathbf { 3 4 } } = 5 \\\mathbf { X } _ { \mathrm { ij } } \geq \mathbf { a } \text { far all } i \text { and } j\end{array}$