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You own a woodworking shop and build a variety of hardwood and softwood tables. Each table goes through the stages of cutting, assembling, and painting

You own a woodworking shop and build a variety of hardwood and softwood tables. Each table goes through the stages of cutting, assembling, and painting (optional for some), and each table requires differing amounts of time to complete each stage. Additionally, each type of table generates a specified profit. As an example, a cherry (unpainted) table requires 1.5 hours to cut, 4 hours to assemble, and 0 hours to paint, producing a profit of $60.

In the table below, you will see the required hours for every table in each stage. You will also see specified profits. There is a maximum amount of hours the company can spend in each stage each month, and there is also a certain monthly demand associated with each table. If you make more tables than the market demands, those tables will not be sold. You also have a minimum amount of each type of table that you want to make to be able to meet your customers' needs. Your goal is to maximize profits by following the above criteria.

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\begin{tabular}{|l|r|r|r|rr|} \hline \multicolumn{1}{|c|}{ Type } & \multicolumn{3}{|c|}{ Hours Table } & \\ & \multicolumn{1}{|c|}{ Cutting } & \multicolumn{1}{c|}{ Asembling } & \multicolumn{1}{c|}{ Painting } & Profit \\ \hline Birch & 2 & 3 & 2.5 & $ & 75.00 \\ \hline Cherry & 1.5 & 4 & 3.5 & $ & 85.00 \\ \hline Cherry (Unpainted) & 1.5 & 4 & x & $ & 60.00 \\ \hline Oak & 2 & 4 & 3 & $ & 65.00 \\ \hline Oak (Unpainted) & 2 & 4 & x & $ & 55.00 \\ \hline Walnut & 1 & 2.5 & 3 & $ & 70.00 \\ \hline Max Hours/Month & 175 & 300 & 150 & \\ \hline Total Time Used & 0 & 0 & 0 & \\ \hline \end{tabular} \begin{tabular}{|l|l|r|r|} \hline Type & Count & Demand & Minimum to Produce \\ \hline Birch & & 30 & 5 \\ \hline Cherry & & 20 & 10 \\ \hline Cherry (Unpainted) & & 10 & 5 \\ \hline Oak & & 25 & 20 \\ \hline Oak (Unpainted) & & 15 & 10 \\ \hline Walnut & & 20 & 5 \\ \hline \end{tabular} \begin{tabular}{|l|} \hline Total Profit \\ \hline$ \\ \hline \end{tabular} \begin{tabular}{|l|r|r|r|rr|} \hline \multicolumn{1}{|c|}{ Type } & \multicolumn{3}{|c|}{ Hours Table } & \\ & \multicolumn{1}{|c|}{ Cutting } & \multicolumn{1}{c|}{ Asembling } & \multicolumn{1}{c|}{ Painting } & Profit \\ \hline Birch & 2 & 3 & 2.5 & $ & 75.00 \\ \hline Cherry & 1.5 & 4 & 3.5 & $ & 85.00 \\ \hline Cherry (Unpainted) & 1.5 & 4 & x & $ & 60.00 \\ \hline Oak & 2 & 4 & 3 & $ & 65.00 \\ \hline Oak (Unpainted) & 2 & 4 & x & $ & 55.00 \\ \hline Walnut & 1 & 2.5 & 3 & $ & 70.00 \\ \hline Max Hours/Month & 175 & 300 & 150 & \\ \hline Total Time Used & 0 & 0 & 0 & \\ \hline \end{tabular} \begin{tabular}{|l|l|r|r|} \hline Type & Count & Demand & Minimum to Produce \\ \hline Birch & & 30 & 5 \\ \hline Cherry & & 20 & 10 \\ \hline Cherry (Unpainted) & & 10 & 5 \\ \hline Oak & & 25 & 20 \\ \hline Oak (Unpainted) & & 15 & 10 \\ \hline Walnut & & 20 & 5 \\ \hline \end{tabular} \begin{tabular}{|l|} \hline Total Profit \\ \hline$ \\ \hline \end{tabular}

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