$4\mathrm{.}11$ Consider a transportation problem with three supply Table $4\mathrm{.}64$ Transportation Costs

points with supplies $61,82$ and $72,$ and three

demands $72,100$ and $43,$ respectively. The costs are

given in Table $4\mathrm{.}64.$

$($a$)$ Find an initial solution using Vogel's

approximation method.

$($b$)$ Find the optimum solution.