The Monthly Demand for a Certain Brand of Perfume Is

question 222

Multiple Choice

The monthly demand for a certain brand of perfume is given by the demand equation where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when x = 1,000. ​

• A) The rate of change of the price is -3.26 cents per bottle.
• B) The rate of change of the price is -2.46 cents per bottle.
• C) The rate of change of the price is 4.92 cents per bottle.
• D) The rate of change of the price is -10.46 cents per bottle.

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Definitions:

Equilibrium

A state in economic models where supply equals demand, leading to a stable market price and quantity.

Positive Profits

Financial gains realized when the total revenues of a business exceed its total costs.

Pure Monopolist

A single seller in a market that produces a unique product without close substitutes, having significant control over the market price.

Profit-Maximizing Output

The level of production at which a company achieves the highest possible profit, where marginal cost equals marginal revenue.