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.
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.
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