The Pinewood Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Montreal. The plant uses three main resources to make furniture€”wood, upholstery, and labour. The resource requirements for each piece of furniture and the total resources available weekly are as follows:

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 500 pieces of furniture; however, a sofa takes up twice as much space as a table or chair. Each sofa earns $320 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 in order to maximize profit. Formulate and solve a linear programming model for this problem.

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Resource Requirements Furniture Product Wood (kg) Upholstery (m) Labour (hour) Sofa 12 Table 5 Chair Total available 2250 1000 240 resources