Franklin Furniture

Franklin Furniture produces tables and chairs at its East-side plant for use in university classrooms. The unit profit for tables is $70, while that for chairs is $30.

Tables and chairs are manufactured using finished pressed wood and polished aluminum fittings. Including scrap, each table uses 20 square feet of pressed wood, whereas each chair uses 12.5 square feet of the pressed wood. Franklin Furniture has 6000 square feet of the pressed weed available for the East-side plant weekly. The aluminum fittings that reinforce the legs of both the tables and chairs are purchased from an outside supplier. Franklin Furniture can purchase up to 400 boxes of fittings weekly; one box is required for each table or chair manufactured.

Production time is 72 minutes (1.2 hours) per table and 18 minutes (0.3 hours) per chair. Franklin Furniture has eight employees, each of whom works an average of 7.5 hours per day. Thus, in an average five-day work week, the company has available 8(7.5)(5) = 300 production hours.

Franklin Furniture also produces desks and computer workstations at its West-side plant. Each desk nets the company a profit of $100, while each computer workstation nets $125. These products are also produced from finished pressed wood and aluminum. The amount of each, as well as the labor time needed to produce a desk or computer workstation, is given in the following table.

Pressed Wood Aluminum Fittings Labor Desk 20 sq. ft. 1 box 1.5 hours Workstations 30 sq. ft. 1 box 2.0 hours Available 6000 sq. ft. 400 boxes 300 hours

Franklin Furniture is considering combining operations of both plants into a single plant. This consolidation will combine the weekly available resources so that 12,000 square feet of pressed wood, 800 boxes of aluminum fittings, and 600 production hours will available weekly. However, the accounting department estimates the cost of renovating the plant will be $5000 per week, on an amortized basis.

In your role of a Business Consultant to Franklin Furniture, prepare a business report for Franklin Furniture giving optimal weekly production schedules for each of its plants operating separately. Then include an analysis and recommendation to Franklin Furniture for combining operations at both plants into a single plant.

(Hint: This case can be solved by splitting it into three small cases, two of which can be analyzed using only two decision variables.)

Source: Lawrence, J., and Pasternack, B., Applied Management Science, 2nd Edition Wiley, 2005.

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