Solve the Problem $R$ (In Dollars) Is $R ( p ) = - 5 p ^ { 2 } + 1850 p$

question 323

Multiple Choice

Solve the problem.
-The manufacturer of a CD player has found that the revenue $R$ (in dollars) is $R ( p ) = - 5 p ^ { 2 } + 1850 p$ , when the unit price is p dollars. If the manufacturer sets the price $p$ to maximize revenue, what is the maximum revenue to the nearest whole dollar?

• A) \(\$ 171,125\)
• B) \(\$ 342,250\)
• C) \(\$ 684,500\)
• D) \(\$ 1,369,000\)

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Definitions:

Positive Amount

A value that is greater than zero, indicating a quantity that adds to a total rather than subtracting from it.

Price

The financial charge expected, required, or dispensed as payment for a product.

Marginal Cost Curve

A graph that shows the change in the total cost of producing one additional unit of a good or service.

Average Fixed Cost Curve

A graphical representation showing how the average fixed cost per unit changes as the quantity of output produced changes.