Solve the Problem $z = 10 x ^ { 2 } + 2 y ^ { 2 }$

question 38

Multiple Choice

Solve the problem.
-Write parametric equations for the tangent line to the curve of intersection of the surfaces $z = 10 x ^ { 2 } + 2 y ^ { 2 }$ and $z = x + y + 10$ at the point $( 1,1,12 )$ .

• A) x = -19t + 1, y = 21t + 1, z = 16t + 12
• B) x = -3t + 1, y = 21t + 1, z = 16t + 12
• C) x = -19t + 1, y = 19t + 1, z = 16t + 12
• D) x = -3t + 1, y = 19t + 1, z = 16t + 12

Comprehend the significance and calculation of average variable costs and their role in maximizing profits.

Grasp the importance of identifying the profit-maximizing price and quantity in various market scenarios.

Recognize the conditions and calculations related to a firm’s shutdown point.

Calculate and evaluate the financial requirements to achieve a desired return on investment in diverse business scenarios.

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Definitions:

Predetermined Overhead Rate

This rate is calculated before the period begins and is used to apply manufacturing overhead costs to products based on a consistent formula.

Fixed Manufacturing Overhead

Costs in manufacturing that do not vary with the level of production, including factory rent, salaries of permanent staff, and equipment depreciation.

Machine-Hours

A measure of the amount of time machines are operated in the manufacturing process, used as a basis for allocating costs.

Predetermined Overhead Rate

A rate calculated before a period begins, used to allocate manufacturing overhead costs to products based on a selected activity base such as labor hours or machine hours.