Locate the Local Minimum of the Function $f ( x , y ) = x y + \frac { 4 } { x } + \frac { 4 } { y }$

question 49

Multiple Choice

Locate the local minimum of the function. $f ( x , y ) = x y + \frac { 4 } { x } + \frac { 4 } { y }$

• A) \(\left( 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 1 } { 3 } } , 3 \cdot 64 ^ { \frac { 2 } { 3 } } \right)\)
• B) \(\left( 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 1 } { 3 } } , 12 ^ { \frac { 2 } { 3 } } \right)\)
• C) \(\left( 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 2 } { 3 } } \right)\)
• D) \(\left( 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 1 } { 3 } } , 3 \cdot 4 ^ { \frac { 2 } { 3 } } \right)\)
• E) \(\left( 4 ^ { \frac { 1 } { 3 } } , 4 ^ { \frac { 1 } { 3 } } , 3 \cdot 4 ^ { \frac { 1 } { 3 } } \right)\)

---

Definitions:

Actual Overhead Costs

The real expenses incurred in the manufacturing process that are not directly tied to production, such as utilities and rent for factory space.

Overhead Variances

Differences between the actual overhead costs incurred and the standard costs for the overheads that were budgeted for a period.

Controllable

Controllable usually refers to expenses or costs that can be managed or influenced by decisions made by a company or an individual.

Volume

Refers to the amount of an asset or security that changes hands over a set period of time, commonly used in financial markets to gauge trading activity and liquidity.