A furniture company produces tables, chairs, and sofas. The company uses lumber, fabric, and glass to produce these products. Labor performs the cutting, sanding, and assembly operations. The following table provides the resouce requirents of products.

The selling price of a table is £180, of a chair is £230, and of a sofa is £380. The monthly demand for tables is at most 400, chairs, 500 and sofas, 380. The company pays the laborers £50,000 per month. The amount of labor time used for sanding should not exceed 25% of labor time. Every table is sold with exactly 2 chairs.
a. Formulate a linear programming model.
b. Solve the model by using the computer.

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Resource/Activity Lumber (in board feet) Fabric cutting time in min. Sanding time min. Assembly time in min. Tables 10 24 42 Chairs Sofas 4 6 15 6 60 30 36 36 Available 4000 board ft 250 hours 300 hours 650 hours