A batch distillation facility has a bank of columns of Type 1 and another bank of Type 2. Type 1 columns are available for processing \(6,000 \mathrm{hr} /\) week, and Type 2 columns are available for \(10,000 \mathrm{hr} /\) week. It is desired to use these columns to manufacture two different products, A and B. Distillation time to produce \(100 \mathrm{gal}\) of product A is \(2 \mathrm{hr}\) on Type 1 columns and \(1 \mathrm{hr}\) on Type 2 columns. Distillation time to produce \(100 \mathrm{gal}\) of product \(\mathrm{B}\) is \(1 \mathrm{hr}\) on Type 1 columns and \(4 \mathrm{hr}\) on Type 2 columns. The net profit is \(\$ 5.00 / \mathrm{gal}\) for product A and \(\$ 3.50 / \mathrm{gal}\) for product B. Use an LP with a graph to determine the production schedule that maximizes the net profit in \$/week.