Answer must be completed using Python

SteelCo manufactures three types of steel at two different steel mills. During a given month, Mill 1 has 200 hours of blast furnace time available, whereas Mill 2 has 300 hours. Because of differences in the furnaces at each mill, the time and cost to produce a ton of steel differs for each mill and are shown in the following table. Each month, SteelCo must manufacture a total of at least 400 tons of Steel 1, 500 tons of Steel 2, and 300 tons of Steel 3 to meet demand; however, the total amount of Steel 2 manufactured should not exceed the combined amount of Steel 1 and Steel 3. Also, in order to maintain a roughly uniform usage of the two mills, managements policy is that the percentage of available blast furnace capacity (time) used at each mill should be the same. Clearly formulate a linear program (LP) to minimize the cost of manufacturing the desired steel.

\begin{tabular}{|c|c|c|c|c|c|c|} \hline \multirow{2}{*}{ Mill } & \multicolumn{2}{|c|}{ Steel 1 } & \multicolumn{2}{c|}{ Steel 2 } & \multicolumn{2}{c|}{ Steel 3 } \\ \cline { 2 - 7 } & Cost (\$) & Time (Min) & Cost (\$) & Time (Min) & Cost (\$) & Time (Min) \\ \hline Mill 1 & 10 & 20 & 11 & 22 & 14 & 28 \\ \hline Mill 2 & 12 & 24 & 9 & 18 & 10 & 30 \\ \hline \end{tabular}