Specialties manufactures parts for the furniture industry. The marketing department is predicting sales of exactly 8700 of each of these parts in the next quarter. These three parts are a lumbar support, footrest bracket, and a recline mechanism. Some of these components will have to be purchased from outside suppliers due to limited in-house manufacturing capacity. The supplier can supply a maximum of 4,500 units for any of these parts. The supplier has does have a limit on the total number of parts they can supply. They can supply a total of 9.700 total parts (all three combined) to Specialties.

The cost to purchase these parts from suppliers is in the table below:

PURCHASE COST FROM SUPPLIERS Lumbar Support $11.45 Footrest Bracket $7.35 Recline Mechanism $10.63

Specialties plant consists of three departments. Each one of these parts that is manufactured must be processed in all three departments. The time requirements in hours for each component in each department if manufactured in-house are summarized in the following table.

The hours available for production of these parts are listed in the last row.

COMPONENT Assembly Dept. (hrs./unit) Finishing Dept. (hrs./unit) Fabrication Dept. (hrs./unit) Lumbar Support 0.22 0.24 0.21 Footrest Bracket 0.14 0.12 0.21 Recline Mechanism 0.15 0.21 0.24 Capacity (hrs.) 3500 3500 3800

The cost of producing a part at Specialties is based on the number of hours a part spends in a department and the cost per hour that the department charges for its operation. Note that these costs do not apply when purchasing a part from a supplier - these costs only apply to internally manufactured parts.

Operating costs are: Assembly Dept. 14.75($/hr) Finishing Dept. 18.50(($/hr) FABRICATION Dept. 16.30($/hr)

The revenue generated per part is the same whether you manufacture the part in Specialties manufacturing facility or buy the part from a supplier and is shown below: COMPONENT Revenue ($/part) Lumbar Support 15.21 Footrest Bracket 14.49 Recline Mechanism 16.75

SOLUTION: The optimal solution, the value of the profit, should be $153,270.71

Please list

Objective Function

Constraints

Profit figures