A furniture manufacturer produces high-quality end tables and chairs using mahogany wood. An end table produced by the furniture manufacturer yields a profit of $15 per table, and each chair yields a profit of $20. During any given week of production, resources in the form of 100 hours of skilled labor and 400 square feet of mahogany wood are available. Each end table requires 4 hours of skilled labor and 16 square feet of mahogany wood. Each chair requires 6 hours of skilled labor and 12 square feet of mahogany. Formulate this product mixture problem as a linear programming model, and solve the problem using the graphical method. How many end tables and chairs should be produced to maximize profits? What is the maximum profit for the optimal solution?