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:

Short Bone

A type of bone that is as wide as it is long, providing support and stability with little movement, such as the bones in the wrist and ankle.

Flat Bone

Bones characterized by their thin, flattened structure, usually providing protection and large areas for muscular attachment, such as the skull and ribs.

Epiphyseal Plate

A hyaline cartilage plate in the metaphysis at each end of a long bone, where growth in length occurs.

Hyaline Cartilage

A translucent, bluish-white type of cartilage present in the joints, respiratory tract, and embryonic skeleton, providing support and flexibility.