A large textile company has 2 manufacturing plants, two sources of raw material, and three sales centers. Transportation costs between material sources raw and the plants, and between the plants and the sales centers are the following (data in [$/ton]):

Weekly there are 22 tons of raw materials available in Source 1 and 20 tons at Source 2. Plant 1 can process a maximum of 18 tons of raw material, while plant 2 has a capacity maximum of 14 tons per week. In plants a process of transformation, where each ton of raw material is transformed into 0.9 tons of product. The sales price of the product depends on the sales center. For the center of sales 1 the price is $9 per ton of product; for sales center 2 price is $8 per ton; and for sales center 3 it is $7 per ton. The three sales centers require 8, 14 and 4 tons of product each week respectively. Formulate the linear programming model that allows the textile company plan your transportation and manufacturing operations to meet the requirements of sales centers.

\begin{tabular}{|c|c|c|c|} \hline & & \multicolumn{2}{|c|}{ Plants } \\ \hline \multirow{3}{*}{ Raw material } & & A & B \\ \cline { 2 - 4 } & 1 & 1 & 1,5 \\ \cline { 2 - 4 } & 2 & 2 & 1,5 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|} \hline & & \multicolumn{3}{|c|}{ Sales Center } \\ \hline \multirow{3}{*}{ Plants } & & 1 & 2 & 3 \\ \cline { 2 - 5 } & A & 4 & 2 & 1 \\ \cline { 2 - 5 } & B & 3 & 4 & 2 \\ \hline \end{tabular}