Evaluate $\iint _ { S } f ( x , y , z ) d S$

question 29

Multiple Choice

Evaluate $\iint _ { S } f ( x , y , z ) d S$ . $f ( x , y , z ) = 5 x + 6 y + z$ ; S is the part of the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ between the planes $z = 1$ and $z = 4$ .

• A) \(126 \pi \sqrt { 2 }\)
• B) \(42\) \(\pi \sqrt { 2 }\)
• C) \(126 \sqrt { 2 }\)
• D) 0

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Definitions:

Degree of Operating Leverage

A financial ratio that measures the percentage change in operating income in response to a percentage change in sales.

Forecasted Contribution Margin

An estimated metric that indicates the difference between sales revenue and variable costs of goods sold, used to predict the profitability of sales.

Contribution Margin

The difference between sales revenue and variable costs, used to cover fixed costs and to generate profit.

Contribution Margin

The selling price per unit, minus the variable cost per unit, indicating how much each unit contributes to covering fixed costs and generating profit.