Swearingen and McDonald, small furniture manufacturer, produces fine hardwood tables and chairs. Each product should go through three stages in the manufacturing procedure assembly, finishing, and inspection. Each table needs 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection. Each and every chair needs 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection. The profit for each table is $150 while the profit per chair is $100. Currently, each week there're 300 hours of assembly time available, 220 hours of finishing time, and 30 hours of inspection time. To keep balance, the number of chairs produced must be at least twice the number of tables. Also, the number of chairs can't exceed 6 times the number of tables. Formulate this as a linear programming problem. Carefully illustrate all decision variables. Find the solution.