Evaluate the Integral $$\int _ { 0 } ^ { 3 } \int _ { 0 } ^ { 9 ( 1 - z / 3 ) } \int _ { 0 } ^ { 7 ( 1 - y / 9 - z / 3 ) } d x d y d z$$

question 38

Multiple Choice

Evaluate the integral.
- $$\int _ { 0 } ^ { 3 } \int _ { 0 } ^ { 9 ( 1 - z / 3 ) } \int _ { 0 } ^ { 7 ( 1 - y / 9 - z / 3 ) } d x d y d z$$

• A) 63
• B) \(\frac { 189 } { 4 }\)
• C) \(\frac { 63 } { 2 }\)
• D) \(\frac { 189 } { 8 }\)

---

Definitions:

Planning Budget

A budget created for a specific level of activity; it helps managers plan the expected revenues, costs, and profits for different levels of operational activity.

Total Variable Cost

The cumulative cost that varies in direct proportion to changes in the level of output or activity, such as raw materials and direct labor.

Total Expenses

The aggregate amount of all costs incurred by a business during a specific period.

Flexible Budget

A budget that adjusts or flexes with changes in volume or activity, providing a more useful tool for performance evaluation.