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:
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Resource Requirements
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Wood (board ft.)
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Upholstery (yd.)
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Labor (hr.)
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Sofa
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7
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12
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6
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Table
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5
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--
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9
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Chair
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4
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7
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5
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Total available resources
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2,250
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1,000
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240
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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.