Use the Given Transformation to Evaluate the Integral $$\begin{aligned}u = & 2 x + y - z , v = - x + y + z , w = - x + y + 2 z \\& \iiint _ { R } ( 2 x + y - z ) d x d y d z\end{aligned}$$

question 261

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{aligned}u = & 2 x + y - z , v = - x + y + z , w = - x + y + 2 z \\& \iiint _ { R } ( 2 x + y - z ) d x d y d z\end{aligned}$$
where $R$ is the parallelepiped bounded by the planes $2 x + y - z = 6,2 x + y - z = 9 , - x + y + z = 2 , - x + y + z = 4$ , $- x + y + 2 z = 6 , - x + y + 2 z = 7$

• A) 15
• B) \(\frac { 45 } { 2 }\)
• C) 135
• D) 60

---

Definitions:

Factory Overhead

Indirect costs associated with manufacturing, including utilities, depreciation of equipment, and salaries of managers.

Management Process

A systematic approach to managing and optimizing an organization's resources and operations towards achieving its objectives.

Alternative Actions

Different courses of action or strategies that can be taken in a given situation.

Decision Making

A component inherent in the other management processes of planning, directing, controlling, and improving.