The management of Lorimar Watch Company has determined that...

The management of Lorimar Watch Company has determined that the daily marginal revenue function associated with producing and selling their travel clocks is given by $$R^{\prime}(x)=-0.009 x+12$$ where $x$ denotes the number of units produced and sold and $R^{\prime}(x)$ is measured in dollars per unit. a. Determine the revenue function $R(x)$ associated with producing and selling these clocks. b. What is the demand equation that relates the wholesale unit price with the quantity of travel clocks demanded?

The management of Lorimar Watch Company has determined that the daily marginal revenue function associated with producing and selling their travel clocks is given by $$R^{\prime}(x)=-0.009 x+12$$ where $x$ denotes the number of units produced and sold and $R^{\prime}(x)$ is measured in dollars per unit.
a. Determine the revenue function $R(x)$ associated with producing and selling these clocks.
b. What is the demand equation that relates the wholesale unit price with the quantity of travel clocks demanded?

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Key Concepts

Integration to Determine the Revenue Function

Integration is used to recover the total revenue function from its marginal revenue function. By integrating the derivative of revenue with respect to quantity, one obtains the accumulated revenue, up to an arbitrary constant representing fixed or initial revenue. This process is a fundamental application of calculus in economics.

Demand Equation

The demand equation expresses the relationship between the unit price and the quantity demanded. Typically showing an inverse relationship, it is crucial for understanding market behavior, setting prices, and making supply decisions. The demand equation is derived from revenue or marginal revenue functions and reflects how changes in quantity affect the price consumers are willing to pay.

Marginal Revenue

Marginal revenue represents the additional revenue generated from selling one more unit of a product. It is the derivative of the revenue function with respect to quantity, and understanding it is essential for determining optimal production levels and pricing strategies in economic analysis.

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