A manufacturing company has three branches: B$1,$ B$2$ and B$3$ in three different places. The weekly productivity $($counted by total weights $($ton$)$ of the products$)$ for each of the branches is $7$ ton in B$1,4$ ton in B$2$ and $9$ ton in B$3.$ The company needs to transport the products made in three branches to four distribution centers, D$1,$ D$2,$ D$3$ and D$4,$ which are located in four different cities. The demands for each of the four distribution centers is $3$ ton for D$1,6$ ton for D$2,5$ ton for D$3$ and $6$ ton for D$4.$ The transportation prices are shown in Table $1.$ Table $1$ Branch D$1(100$$$/$ton$)$ Distribution Center $317$ D$2($$$100/$ton$)1194$ D$3($$$100/$ton$)$ D$4($$$100/$ton$)1085$ B$13/$ B$2210$ B$3$ Use Vogel's method to find a transportation schedule which aims to minimize the company's transportation cost. $($Hint: the solution is not necessary to be the optimal one.$)$