$\text { Find } \mathrm { f } _ { \mathbf { x } } , \mathrm { f } _ { \mathbf { y } } \text {, and } \mathrm { f } _ { \mathbf { Z } }$

question 346

Multiple Choice

$\text { Find } \mathrm { f } _ { \mathbf { x } } , \mathrm { f } _ { \mathbf { y } } \text {, and } \mathrm { f } _ { \mathbf { Z } }$
- $$f ( x , y , z ) = \frac { z } { \sqrt { x + y ^ { 2 } } }$$

• A) \(f _ { x } = \frac { z } { 2 \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { y } = \frac { y z } { \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { z } = \frac { 1 } { \sqrt { x + y ^ { 2 } } }\)
• B) \(f _ { x } = - \frac { z } { 2 \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { y } = \frac { y z } { \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { z } = - \frac { 1 } { \sqrt { x + y ^ { 2 } } }\)
• C) \(f _ { x } = \frac { z } { 2 \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { y } = - \frac { y z } { \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { z } = \frac { 1 } { \sqrt { x + y ^ { 2 } } }\)
• D) \(f _ { x } = - \frac { z } { 2 \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { y } = - \frac { y z } { \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { z } = \frac { 1 } { \sqrt { x + y ^ { 2 } } }\)

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Definitions:

Predetermined Overhead Rate

A rate used to apply manufacturing overhead to products or services, calculated before the accounting period begins based on estimated costs.

Fixed Manufacturing Overhead

Costs that do not vary with the level of production or sales, including expenses like rent, salaries, and utilities.

Absorption Costing

An accounting approach that includes all manufacturing costs (both variable and fixed) in the cost of a product, used for external reporting.

Plantwide Overhead Rate

A single overhead rate calculated by dividing total factory overhead by the total amount of the allocation base used across the entire plant.