(2) Economic considerations in manufacturing process.

We have an incentive in forming the box to make a large contained volume but we also have costs associated with this manufacturing process.

We can charge $0.10/in^3 for the box.

The costs of materials is $0.015/square inch when new and any scrap left over from the process will be generating $0.004/square inch.

We note that on the box we need to file and glue the eight vertical edges at a cost of $0.01/linear inch, file all exposed edges (the three edges of the open top and the open flap itself) at a cost of $0.02/linear inch, and insert hinges in the open flap edge. The latter is a fixed cost of $0.40 no matter what geometry we use.

Now, find the dimensions of the enclosed box which will make profit maximum.

Recall Profit = Revenue - Cost.