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:

Resource Requirements Wood (board ft.) 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 type of furniture to make per week to maximize profit.

a. Formulate a linear programming model for this problem.

b. Solve the model by using the computer. LO.1