Solve the Given Problem by Using Substitution $f ( x , y , z ) = 8 - x ^ { 2 } - y ^ { 2 } - z ^ { 2 }$

question 107

Multiple Choice

Solve the given problem by using substitution.
Find the maximum value of $f ( x , y , z ) = 8 - x ^ { 2 } - y ^ { 2 } - z ^ { 2 }$ subject to $z = 3 y$ .

• A) \(f _ { \max } = 8\)
• B) \(f _ { \max } = 9\)
• C) \(f _ { \max } = 3\)
• D) \(f _ { \max } = 10\)
• E) \(f _ { \max } = 7\)

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Definitions:

Fixed Costs

Overheads such as rent, salaries, and insurance that do not fluctuate with changes in the volume of production or sales.

Break-even Point

The level of sales at which total revenues equal total costs, resulting in no profit or loss and marking the threshold for profitability.

Variable Cost

Expenses that change in proportion to the activity of a business, such as costs for raw materials or production volume.

Fixed Costs

Expenses that remain constant regardless of the amount of goods produced or sold, including lease payments, wages, and insurance premiums.