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 \(\left( 6 , - \frac { 9 } { 2 } , \frac { 225 } { 24 } \right)\)

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Definitions:

Cash Equivalents

Short-term, highly liquid investments such as Treasury bills, commercial paper, and money market funds, that are made solely for the purpose of generating a return on temporarily idle funds.

Cash Flows

The total amount of money being transferred into and out of a business, especially as affecting liquidity.

Indirect Method

An approach used in cash flow statements to adjust net income for changes in non-cash items to calculate cash provided by operating activities.

Operating Activities

Transactions and events that pertain to the core business functions of an organization, influencing net income.