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# Management Science

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 round 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 \$120 in profit. Most people who buy a table also want four chairs to go 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.

The Jacobsons in problem 24 have been approached by a home furnishings company that needs a wooden stool for its catalog. The company has asked the Jacobsons to produce a batch of 20 wooden stools, and the Jacobsons would realize a profit of \$65 for each stool. A stool will require 4 board feet of wood and 5 hours to produce. Formulate and solve an integer programming model to help the Jacobsons determine if they should produce the stools.

#### Solution Preview

Step 1: Problem description: Evaluate additional order for stools. Notice that this order is for fixed quantity of 20 stools. The decision is to whether to accept the order or not.

Step 2: Define decision variables: Let x1 and x2 be the number of tables and chairs manufactured and sold.
Let y be the indicator variable for the order. The variable y will take value of 1 if order is accepted and 0 otherwise.

Step 3: Formulate objective function: The objective is to maximize profits
Profit = per unit profit for ...

#### Solution Summary

Solution contains formulation and optimal solution of an integer programming model to help the Jacobsons determine if they should produce the stools.

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