A Rectangular Box Having a Top and a Square Base

question 42

Essay

A rectangular box having a top and a square base is to be constructed at a cost of $1. If the material for the bottom costs $0.35 per square foot, the material for the top costs $0.15 per square foot, and the material for the sides costs $0.20 per square foot, find the dimensions and volume of the box of maximum volume that can be constructed.

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Definitions:

Machine Hours

A measure of the amount of time a machine is operated, used as a basis for allocating factory overhead costs to products.

Standard Cost

A predetermined cost of manufacturing a product or performing a service, used as a benchmark to measure performance.

Direct Labor

The cost of the work performed by employees directly involved in manufacturing a product or providing a service.

Time Variance

The gap between the time actually needed to accomplish a task and the time that was anticipated for it.