Question: #16 The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Greensboro, NC. 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:

RESOURCE REQUIREMENTS

Wood (lb) upholstery (yd) labor (hr)

Sofa 7 12 6

Table 5 --- 9

Chair 4 7 5

Total available

resources 2250 1000 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 earns $275, and each chair, $190. The company wants to know how many pieces of each type 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.