If Y = C ( X ) Represents the Cost

question 33

Multiple Choice

If y = c ( x ) represents the cost of producing x units in a manufacturing process, the elasticity of cost is defined as $E ( x ) = \frac { \text { marginal cost } } { \text { average cost } } = \frac { C ^ { \prime } ( x ) } { C ( x ) / x } = \frac { x } { y } \frac { d y } { d x }$ . Find the cost function if the elasticity function is $E ( x ) = \frac { 12 x - y } { 2 y - 6 x }$ , where $C ( 90 ) = 272$ and $x \geq 90$ .

• A) \(y = \frac { 3 \left( x ^ { 2 } + \sqrt { x ^ { 4 } - 730,210 x } \right) } { x }\)
• B) \(y = \frac { 6 \left( x ^ { 2 } + \sqrt { x ^ { 4 } - 730,210 x } \right) } { x }\)
• C) \(y = \frac { 6 \left( x ^ { 2 } + \sqrt { x ^ { 4 } - 728,960 } \right) } { x }\)
• D) \(y = \frac { 3 \left( x ^ { 2 } + 2 \sqrt { x ^ { 4 } - 734,041 } \right) } { x }\)
• E)\(y = \frac { 3 \left( x ^ { 2 } + \sqrt { x ^ { 4 } - 728,960 x } \right) } { x }\)

---

Definitions:

Balance Sheet

A financial statement that summarizes a company's assets, liabilities, and stockholders' equity at a specific point in time.

Stock Split

An action by a company to divide its existing shares into multiple shares to boost the liquidity of the shares, though the overall value of the shares remains the same.

Retained Earnings

Cumulative earnings of a company that are not distributed to the owners and are reinvested in the business.

2-for-1

Describes a type of stock split where a company divides its existing stock into two shares, effectively doubling the number of shares owned by shareholders but potentially halving the price per share.