An Open Box Is to Be Made from a Square $V ( x ) = - 2 x ^ { 3 } + 28 x ^ { 2 }$

question 52

Multiple Choice

An open box is to be made from a square piece of cardboard,28 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below) .Determine the function,V,in terms of x,that represents the volume of the box.

• A) \(V ( x ) = - 2 x ^ { 3 } + 28 x ^ { 2 }\)
• B) \(V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 }\)
• C) \(V ( x ) = 4 x ^ { 3 } - 56 x ^ { 2 } + 28 x\)
• D) \(V ( x ) = - 4 x ^ { 3 } + 56 x ^ { 2 } - 28 x\)
• E) \(V ( x ) = 4 x ^ { 3 } - 112 x ^ { 2 } + 784 x\)

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Definitions:

ATC Curve

Represents the average total cost of producing a good or service, calculated by dividing total cost by the quantity produced, and typically displayed as a graph.

AVC Curve

The Average Variable Cost curve, which graphs the per unit variable costs of production against the quantity of output.

Average Variable Cost

The total variable costs (such as labor and materials) divided by the quantity of output produced.

Average Total Cost

The total cost of production (fixed plus variable costs) divided by the total quantity of output produced, indicating the cost of producing each unit of output.