Formulate transportation problem as an LP problem. Formulate its dual, and discuss how Dual LP can be used to progress towards optimal solution. In the following table rows correspond to sources to transport from and columns correspond to destinations to transport to$.$ Each cell contains unit transportation cost. Find the initial solution using north west corner rule. Verify whether your solution is optimal $($by verifying dual inequalities$).$ If not improve the solution. Iterate to optimal solution.

Amount at Source

$\backslash$table$[[,$D$1,$D$2,$D$3,$D$4],[$S$1,1,3,2,7,4,100,],[$S$2,5,4,6,1,3,200,],[$S$3,6,2,1,5,2,300,],[$S$4,2,5,7,1,6,400,],[$Demand$,130,150,210,220,290,,]]$