A small furniture manufacturer produces tables, closets 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. Each closet requires 4 hours of assembly, 6 hours of finishing, and 2 hour of inspection. The profit per table is $120, the profit per closet is $160, 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. Formulate this as a linear programming problem.

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