Question

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'(x) = -0.005x⁷, where x denotes the number of units produced and sold and r'(x) is measured in dollars/unit. (a) Determine the revenue function r(x) associated with producing and selling these clocks. r(x) = ?

Answer 1

To find the revenue function r(x) based on the given marginal revenue function r'(x) = -0.005x⁷, integrate the marginal revenue function. The result is r(x) = -0.000625x⁸ + C, where C is a constant of integration that would require additional information to determine.

Step-by-step explanation:

The management of Lorimar Watch Company has determined the daily marginal revenue function for producing and selling their travel clocks is r'(x) = -0.005x⁷, with x representing the number of units produced and sold. To determine the revenue function r(x), we need to integrate the marginal revenue function. The integral of r'(x) = -0.005x⁷ with respect to x gives us r(x), which will be of the form Ax⁸, where A is a constant that represents the initial revenue (with A divided by 8 to compensate for the power during integration).

However, since we were not provided with an initial condition (such as initial revenue when x=0), the revenue function will contain an unknown constant C: r(x) = -0.005/8 x⁸ + C. Without further information, we cannot solve for C, but we have the general form of the revenue function for the Lorimar Watch Company.