Question: False Valley Faux Vintage Reproductions of Fine Furnishings manufactures its Appalachian Antiques line of tables and chairs. Each of these products results from three stages in the manufacturing process: assembly, finishing, and inspection. Each table requires three hours of assembly, two hours of finishing, and one-half hour of inspection; each chair requires two hours of assembly, three hours of finishing, and one hour of inspection. False Valley earns a profit of $120 per table and $80 per chair manufactured and sold. Each week, under the current production schedule, 240 hours are available for assembly, 180 hours for finishing, and 50 hours for inspection. How many tables and how many chairs should False Valley manufacture in order to optimize this business model?

(a) Construct a tabular organizer to summarize this linear programming problem.

(b) Define the variables, the objective function, and then list all constraints, including any reasonable non-negativity restrictions.

(c) Graph the feasible set or solution region, clearly labeling all relevant vertices.

(d) Test the vertices in the objective function.

(e) State the solution, interpreting the results within the original problem context.