A Small Furniture Manufacturer Produces Tables and Chairs

Essay

A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection.Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection.Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection.The profit per table is $120, while the profit per chair is $80.Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time.To keep a balance, the number of chairs produced should be at least twice the number of tables.Also, the number of chairs cannot exceed six times the number of tables.Formulate this as a linear programming problem.Carefully define all decision variables.