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A furniture company produces three products: tables, sofas, and chairs.
These products are processed in five departments: sawing, fabric cutting, sanding, staining, and assembly departments. Tables and chairs are produced from raw lumber only, and the sofas require lumber and fabric. Glue and thread are plentiful and represent a relatively insignificant cost that is included in operating expenses.
The specific requirements for each product are as follows:
Resource or activity Quantity available Table Sofa Chair Lumber (board feet) 4,600 10 8 3.5 Fabric (yards) 2,500 None 10 None Saw lumber (hours) 300 0.5 0.4 0.4 Cut fabric (hours) 150 None 0.4 None Sand (hours) 280 0.4 0.2 0.5 Stain (hours) 200 0.4 0.3 0.4 Assemble (hours) 700 1 2 0.4
The company’s direct labor expenses are $75,000 per month (assume that labor cost is fixed and the firm does not plan to hire or fire employees in the near future). Based on the current demand, the firm can sell up to 300 tables, 250 sofas, and 400 chairs per month. Sales prices are $400 for tables, $650 for sofas, and $235 for chairs.
The variable material costs you should consider are driven by $10 per board feet of lumber, and $17 per yard of fabric.
2.1. Develop a descriptive model that connects between a production mix (decision variables) and profit (objective metric). In order to do so:
-Clearly list all inputs (i.e., decision variables), parameters, and outputs and assign them a symbol if necessary.
-Express the algebraic relationship between inputs/parameters and outputs.
-Express the algebraic relationship between decision variables, production requirements, and available resources and activities.
 
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