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.

$1.$ The margins of the two products are provided in the report submitted by the Accounting Department. Margin is computed by subtracting both variable and fixed costs from sales price. Would you be comfortable using the margin amounts for making decisions related to the metal boxes and aluminum rods? Would you rather use contribution margin instead? Why or why not?

For all questions below, you should provide detailed computations for your answers.

$2.$ Compute the unit contribution margin for:

a$.$ Purchased metal boxes.

b$.$ Manufactured metal boxes.

c$.$ Manufactured aluminum rods.

$3.$ Anner the olivia are astil a ding he boal boxes:

b$.$ Hameruch is ty prun ly cost of Make $($manufacture$)$ and Sell $1$ metal box.

c$.$ How much is Unit Contribution Margin for making $($& selling$)1$ metal box, net of opportunity cost?

$4.$ Which product should be manufactured first? Why?

You should provide computations to justify your answer.

$5.$ Determine:

a$.$ the number units that should be manufactured $($if any$)$ and purchased $($if any$)$ for Metal boxes.

b$.$ the number units that should be manufactured $($if any$)$ for Aluminum rods.

You should provide some production$/$purchase schedule or computations to justify your answer.

$6.$ Compute total contribution margin that would result from the optimal decision $($determined in #$5).$

$7.$ ReProcessAll Inc. is an outside engineering firm. It can revise the production process in such a way that the required processing time on $1$ Metal box is reduced by $10\%($from $6$ hours to $5\mathrm{.}4$ hours$).$ What is the maximum amount that SellaChem would be willing to pay to ReProcessAll Inc. for using the new process?

$8.$ Ignore #$7.$ ExtraProc is an outside company that rents processing machines.

ExtraProc

charges its machine rental fee by the hour of processing time. What would be the highest price

per hour of processing machine time that SellaChem, Inc. is willing to pay to