Posted: December 27th, 2016

Harry and Melissa Jacobson produce handcrafted furniture in a workshop on their farm.

Harry and Melissa Jacobson produce handcrafted furniture in a workshop on their farm. They have obtained a load of 600 board feet of birch from a neighbor and are planning to produce roound kitchen tables and ladder-back chairs during the next three months. Each table will require 30 hours of labor, each chair will require 18 hours, and between them they have a total of 480 hours of labor available. A table requires 40 board feet of wood to make, and a chair requires 15 board feet. A table earns the couple $575 in profit, and a chair earns 0 in profit. Most people who buy a table also want four chairs to got with it, so for every table that is produced at least four chairs must also be made, although additional chairs can also be sold separately. Formulate and solve an integer programming model that will determine the number of tables and chairs the Jacobsons should make to maximize profit.