Find the Cost Function for the Marginal Cost $\frac { d C } { d x } = \frac { 1 } { 40 } x ^ { 2 } + 90$

question 18

Multiple Choice

Find the cost function for the marginal cost $\frac { d C } { d x } = \frac { 1 } { 40 } x ^ { 2 } + 90$ and fixed cost of $\$ 2000$ (for x = 0) .

• A) \(C ( x ) = \frac { 1 } { 80 } x ^ { 3 } + 90 x + 2000\)
• B) \(C ( x ) = \frac { 1 } { 120 } x ^ { 3 } + 2000 x + 90\)
• C) \(C ( x ) = \frac { 1 } { 120 } x ^ { 3 } + 90 x + 2000\)
• D) \(C ( x ) = \frac { 1 } { 80 } x ^ { 4 } + 2000 x + 90\)
• E) \(C ( x ) = \frac { 1 } { 120 } x ^ { 4 } + 90 x + 2000\)

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Definitions:

Deadweight Loss

A loss of economic efficiency that can occur when equilibrium is not achievable or not achieved in a market.

Subsidy

A financial contribution granted by the government or a public body to support businesses or consumers, making goods or services more affordable.

Manure

Organic matter, mainly derived from animal feces, used as fertilizer in agriculture.

Price Elasticity

A measure of the responsiveness of the quantity demanded or supplied of a good or service to a change in its price.