1 A fumiture company produces three products: end tables, sofas, and chairs. These products are processed in five departments: the saw lumber, fabric cutting, sanding, staining, and assembly departments. End tables and chairs are produced from raw lumber only, and the sofas require lum- ber and fabric. Glue and thread are plentiful and represent a relatively insignificant cost that is included in operating expense. The specific requirements for each product are as follows:

The company's direct labor expenses are $75,000 per month for the 1,540 hours of labor, at $48.70 per hour. Based on current demand, the firm can sell 300 end tables, 180 sofas, and 400 chairs per month. Sales prices are $400 for end tables, $750 for sofas, and $240 for chairs. Assume that labor cost is fixed and the firm does not plan to hire or fire any employees over the next month.

a. What is the most limiting resource to the fumiture company?

b. Determine the product mix needed to maximize profit at the fumiture company. What is the optimal number of end tables, sofas, and chairs to produce each month?

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RESOURCE OR ACTIVITY (QUANTITY AVAILABLE PER MONTH) Lumber (4,300 board feet) Fabric (2,500 yards) Saw lumber (280 hours) Cut fabric (140 hours) Sand (280 hours) REQUIRED PER END TABLE 10 board feet @ $10/foot = $100/table None 30 minutes None REQUIRED PER SOFA 75 board feet @ $10/foot = $75 10 yards @ $1750/yard = $175 24 minutes REQUIRED PER CHAIR 4 board feet @ $10/foot=$40 None 30 minutes None 30 minutes 24 minutes 30 minutes 6 minutes Stain (140 hours) 24 minutes 12 minutes 24 minutes Assemble (700 hours) 60 minutes go minutes 30 minutes