The Ordering and Transportation Cost C for Components Used in a Manufacturing

question 50

Multiple Choice

The ordering and transportation cost C for components used in a manufacturing process is approximated by $C ( x ) = 27 \left( \frac { 1 } { x } , \frac { 1 } { x + 2 } \right)$ , where $C$ is measured in thousands of dollars and $x$ is the order size in hundreds. According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval $( 4,6 )$ . Find this order size. Round your answer to three decimal places.

• A) \(9.657\) components
• B) \(6.828\) components
• C) \(8.000\) components
• D) \(6.000\) components
• E) \(4.828\) components

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Definitions:

Net Income

The net earnings of a business once all costs, taxes, and expenses have been deducted from its total income.

Inventory

The total amount of goods a company holds in stock, including raw materials, work-in-progress, and finished goods.

Variable Costing

An accounting method that only assigns variable costs to inventory, considering fixed costs as period expenses.

Absorption Costing

An accounting method that includes all manufacturing costs - direct materials, direct labor, and both variable and fixed overhead - as part of the cost of a product.