A small furniture manufactuere produces fine dining tables and chaires. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2.5 hours of finishing, and 0.5 hours of inspection. Each chair requires 1.5 hours of assembly, 1 hours of finishing, and 0.25 hours of inspection. The profit per table is $165 while the profirt per chair is $28. Currently, each week there ware 310 hours of assembly time available, 280 hours of finishing time, and 140 hours of inspection time. THe dining table and chair are sold as a set of one table and six chairs. Formulate this as a linear programming problem. Carefully define all decision variables.