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/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/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

Marginal Revenue Function

This represents the instantaneous rate of change of the total revenue with respect to the number of units sold. It is essentially the derivative of the revenue function, showing how additional sales affect revenue.

Integration to Recover the Revenue Function

Recovering the revenue function from the marginal revenue function involves integrating the marginal function. Integration reverses differentiation and yields the original revenue function up to an arbitrary constant.

Demand Equation (Price-Quantity Relationship)

The demand equation relates the unit price to the number of units demanded. Usually, it is developed by expressing total revenue as the product of price and quantity, and then solving for the price, reflecting how market price adjusts with changes in quantity.

Constant of Integration

When performing indefinite integration, an arbitrary constant is added to the resulting function. This constant accounts for any fixed revenue not captured by the marginal rates, and it is determined using initial conditions or additional information.

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