Please Solve this without AI$.$ There is a network of energy distribution between sources $($energy producers with

capacities $a_i)$ and users requiring some power $b_j($where ${\displaystyle \underset{i}{\overset{?}{}}}{a}_i={\displaystyle \underset{j}{\overset{?}{}}}{b}_j).$

In order to avoid a big loss, the energy that can be transmitted along each link of the network

is limited; we observe that this constraint makes impossible the satisfaction of all demands.

For each link $(i,j)($where i and $j$ are the vertices in the network which don't necessarily

correspond to a source or a user$),$ we are given the cost $k_{ij}$ of one unit augmentation of the

current energy transmission capacity.

How can we determine the modifications to do on the network so that all the demands are

satisfied and that the cost of the modifications is minimized?

Solve this problem on the above networks. Explain clearly each step of the method used.