Question: False Valley Faux Vintage Reproductions of Fine Furnishings manufactures its Appalachian Antiques line of armoires and pantry cupboards. The armoires require 10 linear feet of maple lumber, 30 linear feet of pine lumber, and 20 square feet of cherry veneers; the pantry cupboards require 20 linear feet of maple lumber, 30 linear feet of pine lumber, and 30 square feet of cherry veneers. Contractual obligations with the company’s suppliers state that they must use at least 80 linear feet of maple lumber, 180 linear feet of pine lumber, and 150 square feet of cherry veneers. Production of these pieces of furniture cost False Valley $300 armoire and $400 per pantry cupboard. How many armoires and pantry cupboards 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.