Find the Extreme Values of the Function Subject to the Given

question 304

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y , z ) = 4 x - 3 y + 2 z , \quad x ^ { 2 } + y ^ { 2 } = 6 z$$

• A) Maximum: none; minimum: \(- \frac { 75 } { 4 }\) at \(\left( - 6 , \frac { 9 } { 2 } , \frac { 225 } { 24 } \right)\)
• B) Maximum: none; minimum: \(\frac { 117 } { 4 }\) at \(\left( 6 , \frac { 9 } { 2 } , \frac { 225 } { 24 } \right)\)
• C) Maximum: none; minimum: \(- \frac { 33 } { 4 }\) at \(\left( 6 , \frac { 9 } { 2 } , - \frac { 225 } { 24 } \right)\)
• D) Maximum: none; minimum: \(\frac { 225 } { 4 }\) at \(\left( 6 , - \frac { 9 } { 2 } , \frac { 225 } { 24 } \right)\)

---

Definitions:

Adjusted Cash Balance

An amount reflecting the true cash balance after accounting for outstanding checks or deposits in transit.

Check Register

A check register is a record book used to track checks written, deposits made, and the current balance of a checking account.

Closed Account

A bank or credit account that has been terminated, either by the customer or the financial institution, often due to inactivity or zero balance.

Bank Statement

A document issued by a bank detailing all transactions in a customer's account over a specified period.