A Rectangular Piece of Cardboard Measuring 20 Inches by 39 $1364.09$

question 17

Multiple Choice

A rectangular piece of cardboard measuring 20 inches by 39 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each
Such square. What is the maximum volume of this box? If necessary, round to 2 decimal places.

• A) \(1364.09\) in. \(^ { 3 }\)
• B) \(29,578.83\) in. 3
• C) \(1490.83\) in. 3
• D) \(631.5 \mathrm { in } ^ { 3 }\)

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Definitions:

Isoquants

Curves on a graph that represent different combinations of inputs that produce the same level of output, used in production theory.

Robot Hours

The amount of time robots are operational and performing tasks or production processes in a manufacturing or service setting.

Labor Hours

Labor hours refer to the total number of hours worked by employees within a given period, used as a measure of labor input in production processes.

Isoquant

A curve that represents all the combinations of inputs that result in the production of a certain level of output, suggesting input substitutability in the production process.