Posted: January 3rd, 2017

The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Greensboro, North Carolina

The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Greensboro, North Carolina. The plant uses three main resources to make furniture-wood, upholstery, and labor. The resource requirements for each piece of furniture and the total resources available weekly are as follows.
Resoucre Requirements

Wood(1b) Upholstery(yd) Labor(hr)
Sofa 7 12 6
Table 5 ? 9
Chair 4 7 5
Total available resources 2,250 1,000 240

The furniture is produced on a weekly basis and stored in a warehouse until the end of the week, when it is shipped out. The warehouse has a total capacity of 650 pieces of furniture. Each sofa earns $400 in profit, each table, $275, and each chair, $190. The company wants to know how many pieces of each tyupe of furniture to make per week to maximize profit.

a. Formulate a linear programming model for this problem.
b. Solve the model using the computer.