The Marginal Cost Function $C ^ { \prime } ( x )$

question 45

Multiple Choice

The marginal cost function $C ^ { \prime } ( x )$ is defined to be the derivative of the cost function. If the marginal cost of manufacturing $x$ units of a product is
$C ^ { \prime } ( x ) = 0.009 x ^ { 2 } - 1.8 x + 9$ (measured in dollars per unit) and the fixed start-up cost is $C ( 0 ) = 2,200,000$ , use the Total Change Theorem to find the cost of producing the first 5,000 units.

• A) \(\$ 354,445,000\)
• B) \(\$ 354,345,000\)
• C) \(\$ 354,845,000\)
• D) \(\$ 354,545,000\)
• E) \(\$ 354,745,000\)

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Definitions:

Fixed Expenses

Costs that do not fluctuate with changes in production level or sales volume, such as rent and salaries.

Absorption Costing

A method of costing that includes all manufacturing costs - direct materials, direct labor, and both variable and fixed manufacturing overhead in the cost of a product.

Net Operating Income

The total operating profit of a company after all operating expenses, excluding taxes and interest expenses, have been deducted from total revenue.

First Year

Refers to the initial period or the first 12 months of a specific timeframe, often used in the context of financial or operational performance.