Question

22. Harry and Melissa Jacobson produce handerafted 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 3 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 to determine the number of tables and chairs the Jacobsons should make to maximize profit.

Answer 1

To maximize profit, the Jacobsons should produce a certain number of tables and chairs. The integer programming model is formulated with the objective function and constraints.

Step-by-step explanation:

To formulate the integer programming model, let:

x = number of tables produced

y = number of chairs produced

The objective function to maximize profit is:

Profit = 575x + 120y

The constraints are:

30x + 18y ≤ 480 (available labor hours)

40x + 15y ≤ 600 (available board feet of birch)

y ≥ 4x (each table must have at least four chairs)

x, y ≥ 0 (tables and chairs cannot be negative)