Room & Board

Room & Board 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 lumber and fabric. Glue and thread are plentiful and represent a relatively insignificant cost that is included in operating costs. The specific requirements for each product are as follows.

Resource or Activity (quantity available per month)

Required per End Table

Required per Sofa

Required per Chair

Lumber (4,350 board feet)

10 board feet

7.5 board feet

4 board feet

Fabric (2,500 yards)

None

10 yards

None

Saw lumber (280 hours)

30 minutes

24 minutes

30 minutes

Cut fabric (140 hours)

None

24 minutes

None

Sand (280 hours)

30 minutes

6 minutes

30 minutes

Stain (140 hours)

24 minutes

12 minutes

24 minutes

Assemble (700 hours)

60 minutes

90 minutes

30 minutes

The company's direct labor expenses are $75,000 per month for the 1,540 hours of labor, at $48.70 per hour. Lumber costs $10 per board foot and fabric costs $17.50 per yard. 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 that the firm does not plan to hire or fire any employees over the next month. Determine the product mix needed to maximize profit at Room & Board.(10 points)