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

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