Question: Adirondack Furniture Company

Adirondack Furniture Company is a small family operated manufacturing company that produces handcrafted casual chairs sold through national retailers. In addition to their primary product, Adirondack also manufactures round dining tables and accompanying chairs from birch wood during a three month period each year. The tables and chairs are marketed through L. L. Bean, a catalog company based in Vermont and are in constant demand. Adirondack has acquired 600 board feet of birch wood for the season and is preparing for the manufacturing period. Each table requires 30 hours of labor and each chair requires 18 hours. A total of 480 hours will be available during the three months. A table requires 40 board feet of wood and a chair requires 15 board feet. Each table contributes $575 to profit and each chair contributes $120. Most table purchases include four chairs although additional chairs are sold separately. L. L. Bean has notified the company that it has a market for handcrafted birch stools and has submitted a contract to Adirondack for 20 stools. The contract would provide a $45 contribution to profit for each stool. A stool would require 4 board feet of wood and 5 hours of labor.

a. Formulate an appropriate linear programming model that can be used to determine the optimal product mix structure for Adirondack Furniture.

b. Determine the optimal product mix including the number of each product manufactured and the total contribution to profit. Provide a narrative of the Management Scientist solution used.