Case: Utilization of a Constrained Resource

SellaChem, Inc., sells a wide range of industrial equipment that are used in factories.

One of the company's products is Metal Box. Production is constrained by the capacity

of an automated processing machine that is used to process the surface. A total of

$3,000$ hours of processing time is available monthly on the machine. Because each box

requires $6$ hours of processing time, monthly production is limited to $500$ boxes. At

present, the processing machine is used exclusively to make the metal boxes. The

accounting department has provided the following financial data concerning the boxes:

Management believes $700$ Boxes could be sold each month if the company had

sufficient processing capacity. As an alternative to adding another processing machine,

management has considered buying additional boxes from an outside supplier. Kinda

Industries, Inc., a supplier of quality products, would be able to provide up to $500$ metal

boxes per month at a price of $$140$ per box, which SellaChem would resell to its

customers at its normal selling price after appropriate relabeling. It has been estimated

that variable selling and administrative expenses amount to $$2$ per metal box whether it

was made or purchased.

Emily Qun, SellaChem's production manager, has suggested that the company could

make better use of the processing machine by manufacturing Aluminum rods, which

would require only $4$ hours of processing time per rod and yet sell for far more than the

boxes. Emily believes that SellaChem could sell up to $200$ rods per month at a price of

$$200$ each. The accounting department has provided the following data concerning the

proposed new product:

The aluminum rods could be produced with existing

equipment and personnel.

As indicated earlier, the company has a processing machine that can give only $3,000$

hours

of processing time. Therefore, it is a constrained resource. Assume that the cost of

using

the processing machine is fixed with respect to processing time. You want to make

decisions in

such a way to maximize the company's profit.