Box Design

Problem: Determine the dimensions for a cabinet to meet various design requirements.

As a manufacturer of electronic equipment, you must design a cabinet for your new product which meets the specifications of various departments within your organisation at minimum cost.

Your engineering department has determined that the equipment requires a volume of at least 1512 cubic inches and that a minimum surface area of 888 square inches will suffice to dissipate heat.

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Marketing will find it easiest to sell the finished device if the footprint of the cabinet is no more than 252 square inches.

Finally, your designers have decreed that for aesthetic reasons, the ratio of height to width should be .618 .1. That is between .518 and .718 inclusively.

The sheet metal from which the cabinet will be made costs $.05 per square inch. Extra labor required on the front and back panels raises the cost for these components to $.10 per square inch.

The objective is to determine the specifications of the box with the smallest production cost.

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